Modeling and Analysis of Two-Part Type Manufacturing Systems

This paper presents a model and analysis of a synchronous tandem flow line that produces different part types on unreliable machines. The machines operate according to a static priority rule, operating on the highest priority part whenever possible, and operating on lower priority parts only when unable to produce those with higher priorities. We develop a new decomposition method to analyze the behavior of the manufacturing system by decomposing the long production line into small analytically tractable components. As a first step in modeling a production line with more than one part type, we restrict ourselves to the case where there are two part types. Detailed modeling and derivations are presented with a small two-part-type production line that consists of two processing machines and two demand machines. Then, a generalized longer flow line is analyzed. Furthermore, estimates for performance measures, such as average buffer levels and production rates, are presented and compared to extensive discrete event simulation. The quantitative behavior of the two-part type processing line under different demand scenarios is also provided.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Consumption of welfare-friendly food products in Great Britain, Italy and Sweden, and how it may be influenced by consumer attitudes to, and behaviour towards, animal welfare attributes

The interest in animal welfare and welfare-friendly food products has been increasing in Europe over the last 10 years. The media, highlighting traditional farming methods and food scares such as those related to salmonella, bovine spongiform encephalopathy/variant Creutzfeldt-Jakob disease (BSE) and avian influenza, have brought the methods of animal farming to public attention. Concerns about farm animal welfare are reflected in the increase in the number of vegetarians and vegans and an increase in consumers wishing to purchase food which is more animal welfare-friendly. This paper considers consumers’ attitudes to animal welfare and to marketing practices, such as product labelling, welfare grading systems and food assurance marks using comparative data collected in a survey of around 1500 consumers in each of Great Britain, Italy and Sweden as part of the EU-funded Welfare Quality research project. The findings suggest a need for the provision of improved consumer information on the welfare provenance of food using appropriate product labelling and other methods.

Conservation and sustainable use of crop wild relatives

Conservation of crop wild relatives (CWRs) is a complex interdisciplinary process that is being addressed by various national and international initiatives, including two Global Environment Facility projects ('In situ Conservation of Crop Wild Relatives through Enhanced Information Management and Field Application' and 'Design, Testing and Evaluation of Best Practices for in situ Conservation of Economically Important Wild Species'), the European Community-funded project 'European Crop Wild Relative Diversity Assessment and Conservation Forum (PGR Forum)' and the European 'In situ and On Farm Network'. The key issues that have arisen are: (1) the definition of what constitutes a CWR, (2) the need for national and regional information systems and a global system, (3) development and application of priority-determining mechanisms, (4) the incorporation of the conservation of CWRs into existing national, regional and international PGR programmes, (5) assessment of the effectiveness of conservation actions, (6) awareness of the importance of CWRs in agricultural development at local, national and international levels both for the scientific and lay communities and (7) policy development and legal framework. The above issues are illustrated by work on the conservation of a group of legumes known as grasspea chicklings, vetchlings, and horticultural ornamental peas (Lathyrus spp.) in their European and Mediterranean centre of diversity. (c) 2007 Published by Elsevier B.V.

Innovative approach to building systems integration problems: Using systems theory, technological forecasting and scenario planning

Building services are worth about 2% GDP and are essential for the effective and efficient operations of the building. It is increasingly recognised that the value of a building is related to the way it supports the client organisation’s ongoing business operations. Building services are central to the functional performance of buildings and provide the necessary conditions for health, well-being, safety and security of the occupants. They frequently comprise several technologically distinct sub-systems and their design and construction requires the involvement of numerous disciplines and trades. Designers and contractors working on the same project are frequently employed by different companies. Materials and equipment is supplied by a diverse range of manufacturers. Facilities managers are responsible for operation of the building service in use. The coordination between these participants is crucially important to achieve optimum performance, but too often is neglected. This leaves room for serious faults. The need for effective integration is important. Modern technology offers increasing opportunities for integrated personal-control systems for lighting, ventilation and security as well as interoperability between systems. Opportunities for a new mode of systems integration are provided by the emergence of PFI/PPP procurements frameworks. This paper attempts to establish how systems integration can be achieved in the process of designing, constructing and operating building services. The essence of the paper therefore is to envisage the emergent organisational responses to the realisation of building services as an interactive systems network.

Trees outside forests and rural livelihoods: a study of Chitwan District, Nepal

Trees outside forests (TOF) in Nepal’s Terai have significantly increased over the past decade. The Chitwan District was one of the focus districts in the Terai Community Forestry Development Project that promoted a tree seedling distribution program. This paper examines the current position of tree integration on farmland and its contribution to livelihoods of rural households in this district. Interviews with local key informants, government and non-government agencies and woodbased industries, as well as an in-depth study of 32 households were used to describe the constraints faced by the households in management of trees on farmland. Most households cited disease, poor growth, lack of preferred tree species, lack of technical support, an uncertain tree market, and lack of financial support as constraints. Despite the important role of trees in subsistence and marketbased rural livelihood diversification, and the consequent reduction in pressure on national forests from on-farm trees, current government policies and practices fail to recognise the value of these trees. It is argued that there is substantial potential for improving on-farm trees to enhance rural livelihoods. A responsive service mechanism centred on tree growing households would help the management of tree resources on the farmland.

A comparison of stratosphere-troposphere transport in convection-permitting and convection-parameterizing simulations of three mesoscale convective systems

The transport of stratospheric air into the troposphere within deep convection was investigated using the Met Office Unified Model version 6.1. Three cases were simulated in which convective systems formed over the UK in the summer of 2005. For each of these three cases, simulations were performed on a grid having 4 km horizontal grid spacing in which the convection was parameterized and on a grid having 1 km horizontal grid spacing, which permitted explicit representation of the largest energy-containing scales of deep convection. Cross-tropopause transport was diagnosed using passive tracers that were initialized above the dynamically defined tropopause (2 potential vorticity unit surface) with a mixing ratio of 1. Although the synoptic-scale environment and triggering mechanisms varied between the cases, the total simulated transport was similar in all three cases. The total stratosphere-to-troposphere transport over the lifetime of the convective systems ranged from 25 to 100 kg/m2 across the simulated convective systems and resolutions, which corresponds to ∼5–20% of the total mass located within a stratospheric column extending 2 km above the tropopause. In all simulations, the transport into the lower troposphere (defined as below 3.5 km elevation) accounted for ∼1% of the total transport across the tropopause. In the 4 km runs most of the transport was due to parameterized convection, whereas in the 1 km runs the transport was due to explicitly resolved convection. The largest difference between the simulations with different resolutions occurred in the one case of midlevel convection considered, in which the total transport in the 1 km grid spacing simulation with explicit convection was 4 times that in the 4 km grid spacing simulation with parameterized convection. Although the total cross-tropopause transport was similar, stratospheric tracer was deposited more deeply to near-surface elevations in the convection-parameterizing simulations than in convection-permitting simulations.

A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

PINCER trial: a cluster randomised trial comparing the effectiveness and cost-effectiveness of a pharmacist-led IT-based intervention with simple feedback in reducing rates of clinically important errors in medicines management in general practices

Background: Medication errors in general practice are an important source of potentially preventable morbidity and mortality. Building on previous descriptive, qualitative and pilot work, we sought to investigate the effectiveness, cost-effectiveness and likely generalisability of a complex pharm acist-led IT-based intervention aiming to improve prescribing safety in general practice. Objectives: We sought to: • Test the hypothesis that a pharmacist-led IT-based complex intervention using educational outreach and practical support is more effective than simple feedback in reducing the proportion of patients at risk from errors in prescribing and medicines management in general practice. • Conduct an economic evaluation of the cost per error avoided, from the perspective of the National Health Service (NHS). • Analyse data recorded by pharmacists, summarising the proportions of patients judged to be at clinical risk, the actions recommended by pharmacists, and actions completed in the practices. • Explore the views and experiences of healthcare professionals and NHS managers concerning the intervention; investigate potential explanations for the observed effects, and inform decisions on the future roll-out of the pharmacist-led intervention • Examine secular trends in the outcome measures of interest allowing for informal comparison between trial practices and practices that did not participate in the trial contributing to the QRESEARCH database. Methods Two-arm cluster randomised controlled trial of 72 English general practices with embedded economic analysis and longitudinal descriptive and qualitative analysis. Informal comparison of the trial findings with a national descriptive study investigating secular trends undertaken using data from practices contributing to the QRESEARCH database. The main outcomes of interest were prescribing errors and medication monitoring errors at six- and 12-months following the intervention. Results: Participants in the pharmacist intervention arm practices were significantly less likely to have been prescribed a non-selective NSAID without a proton pump inhibitor (PPI) if they had a history of peptic ulcer (OR 0.58, 95%CI 0.38, 0.89), to have been prescribed a beta-blocker if they had asthma (OR 0.73, 95% CI 0.58, 0.91) or (in those aged 75 years and older) to have been prescribed an ACE inhibitor or diuretic without a measurement of urea and electrolytes in the last 15 months (OR 0.51, 95% CI 0.34, 0.78). The economic analysis suggests that the PINCER pharmacist intervention has 95% probability of being cost effective if the decision-maker’s ceiling willingness to pay reaches £75 (6 months) or £85 (12 months) per error avoided. The intervention addressed an issue that was important to professionals and their teams and was delivered in a way that was acceptable to practices with minimum disruption of normal work processes. Comparison of the trial findings with changes seen in QRESEARCH practices indicated that any reductions achieved in the simple feedback arm were likely, in the main, to have been related to secular trends rather than the intervention. Conclusions Compared with simple feedback, the pharmacist-led intervention resulted in reductions in proportions of patients at risk of prescribing and monitoring errors for the primary outcome measures and the composite secondary outcome measures at six-months and (with the exception of the NSAID/peptic ulcer outcome measure) 12-months post-intervention. The intervention is acceptable to pharmacists and practices, and is likely to be seen as costeffective by decision makers.

The effect of farming system and fertilisers on pests and natural enemies: A synthesis of current research

Organic agriculture is becoming widespread due to increased consumer demand and regulatory and political support. Organic agriculture can increase arthropod diversity but the response of pests and their natural enemies is variable. Fertiliser is an important component of agricultural systems and its effects on pests and natural enemies will influence agroecosystems. In this study, meta-analysis and vote-counting techniques were used to compare farming system (organic and conventional) and fertiliser effects on arthropod pests and their natural enemies. The meta-analyses indicated that pests generally benefitted from organic techniques, this is particularly evident when experiments were carried out on a smaller scale. Pest responses to organic and conventional fertiliser types were divergent, plant composts benefitted pest arthropods while the opposite was true for manures, this has implications for pest management. Most natural enemy groups responded positively to organic farming although this was not true for Coleopterans. Experimental scale had a prominent impact on natural enemy responses with farm scale studies showing particularly positive effects of organic agriculture on natural enemies. This suggests that it is large scale features of organic agriculture such as landscape heterogeneity that are beneficial to natural enemies. Natural enemy responses to organic fertilisers were positive indicating that field scale management practices including fertiliser can also be important in pest management.

Reaping the benefits: science and the sustainable intensification of global agriculture

Food security is one of this century’s key global challenges. By 2050 the world will require increased crop production in order to feed its predicted 9 billion people. This must be done in the face of changing consumption patterns, the impacts of climate change and the growing scarcity of water and land. Crop production methods will also have to sustain the environment, preserve natural resources and support livelihoods of farmers and rural populations around the world. There is a pressing need for the ‘sustainable intensifi cation’ of global agriculture in which yields are increased without adverse environmental impact and without the cultivation of more land. Addressing the need to secure a food supply for the whole world requires an urgent international effort with a clear sense of long-term challenges and possibilities. Biological science, especially publicly funded science, must play a vital role in the sustainable intensifi cation of food crop production. The UK has a responsibility and the capacity to take a leading role in providing a range of scientifi c solutions to mitigate potential food shortages. This will require signifi cant funding of cross-disciplinary science for food security. The constraints on food crop production are well understood, but differ widely across regions. The availability of water and good soils are major limiting factors. Signifi cant losses in crop yields occur due to pests, diseases and weed competition. The effects of climate change will further exacerbate the stresses on crop plants, potentially leading to dramatic yield reductions. Maintaining and enhancing the diversity of crop genetic resources is vital to facilitate crop breeding and thereby enhance the resilience of food crop production. Addressing these constraints requires technologies and approaches that are underpinned by good science. Some of these technologies build on existing knowledge, while others are completely radical approaches, drawing on genomics and high-throughput analysis. Novel research methods have the potential to contribute to food crop production through both genetic improvement of crops and new crop and soil management practices. Genetic improvements to crops can occur through breeding or genetic modifi cation to introduce a range of desirable traits. The application of genetic methods has the potential to refi ne existing crops and provide incremental improvements. These methods also have the potential to introduce radical and highly signifi cant improvements to crops by increasing photosynthetic effi ciency, reducing the need for nitrogen or other fertilisers and unlocking some of the unrealised potential of crop genomes. The science of crop management and agricultural practice also needs to be given particular emphasis as part of a food security grand challenge. These approaches can address key constraints in existing crop varieties and can be applied widely. Current approaches to maximising production within agricultural systems are unsustainable; new methodologies that utilise all elements of the agricultural system are needed, including better soil management and enhancement and exploitation of populations of benefi cial soil microbes. Agronomy, soil science and agroecology—the relevant sciences—have been neglected in recent years. Past debates about the use of new technologies for agriculture have tended to adopt an either/or approach, emphasising the merits of particular agricultural systems or technological approaches and the downsides of others. This has been seen most obviously with respect to genetically modifi ed (GM) crops, the use of pesticides and the arguments for and against organic modes of production. These debates have failed to acknowledge that there is no technological panacea for the global challenge of sustainable and secure global food production. There will always be trade-offs and local complexities. This report considers both new crop varieties and appropriate agroecological crop and soil management practices and adopts an inclusive approach. No techniques or technologies should be ruled out. Global agriculture demands a diversity of approaches, specific to crops, localities, cultures and other circumstances. Such diversity demands that the breadth of relevant scientific enquiry is equally diverse, and that science needs to be combined with social, economic and political perspectives. In addition to supporting high-quality science, the UK needs to maintain and build its capacity to innovate, in collaboration with international and national research centres. UK scientists and agronomists have in the past played a leading role in disciplines relevant to agriculture, but training in agricultural sciences and related topics has recently suffered from a lack of policy attention and support. Agricultural extension services, connecting farmers with new innovations, have been similarly neglected in the UK and elsewhere. There is a major need to review the support for and provision of extension services, particularly in developing countries. The governance of innovation for agriculture needs to maximise opportunities for increasing production, while at the same time protecting societies, economies and the environment from negative side effects. Regulatory systems need to improve their assessment of benefits. Horizon scanning will ensure proactive consideration of technological options by governments. Assessment of benefi ts, risks and uncertainties should be seen broadly, and should include the wider impacts of new technologies and practices on economies and societies. Public and stakeholder dialogue—with NGOs, scientists and farmers in particular—needs to be a part of all governance frameworks.

Investigating the prevalence and causes of prescribing errors in general practice: the PRACtICe Study

Aim: To determine the prevalence and nature of prescribing errors in general practice; to explore the causes, and to identify defences against error. Methods: 1) Systematic reviews; 2) Retrospective review of unique medication items prescribed over a 12 month period to a 2% sample of patients from 15 general practices in England; 3) Interviews with 34 prescribers regarding 70 potential errors; 15 root cause analyses, and six focus groups involving 46 primary health care team members Results: The study involved examination of 6,048 unique prescription items for 1,777 patients. Prescribing or monitoring errors were detected for one in eight patients, involving around one in 20 of all prescription items. The vast majority of the errors were of mild to moderate severity, with one in 550 items being associated with a severe error. The following factors were associated with increased risk of prescribing or monitoring errors: male gender, age less than 15 years or greater than 64 years, number of unique medication items prescribed, and being prescribed preparations in the following therapeutic areas: cardiovascular, infections, malignant disease and immunosuppression, musculoskeletal, eye, ENT and skin. Prescribing or monitoring errors were not associated with the grade of GP or whether prescriptions were issued as acute or repeat items. A wide range of underlying causes of error were identified relating to the prescriber, patient, the team, the working environment, the task, the computer system and the primary/secondary care interface. Many defences against error were also identified, including strategies employed by individual prescribers and primary care teams, and making best use of health information technology. Conclusion: Prescribing errors in general practices are common, although severe errors are unusual. Many factors increase the risk of error. Strategies for reducing the prevalence of error should focus on GP training, continuing professional development for GPs, clinical governance, effective use of clinical computer systems, and improving safety systems within general practices and at the interface with secondary care.

Disentangling multi-level systems: averaging, correlations and memory

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way of parameterizing the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long term statistics rather than on the finite-time behavior. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second-order contributions of the fluctuations in the coupling, which can be parameterized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed for disentangling the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exists, can be used equally well to study the statistics of the slow variables and that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multi-level systems.

Duality, observability, and controllability for linear time-varying descriptor systems

A characterization of observability for linear time-varying descriptor systemsE(t)x(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the formE(t)x(t)+F(t)x(t)=f(tt).