Stochastic stability of nonlinear discrete-time Markovian jump systems with time-varying delay and partially unknown transition rates

This paper is concerned with stochastic stability of a class of nonlinear discrete-time Markovian jump systems with interval time-varying delay and partially unknown transition probabilities. A new weighted summation inequality is first derived. We then employ the newly derived inequality to establish delay-dependent conditions which guarantee the stochastic stability of the system. These conditions are derived in terms of tractable matrix inequalities which can be computationally solved by various convex optimized algorithms. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Novel criteria for exponential stability of linear neutral time-varying differential systems

Using a novel approach, we get explicit criteria for exponential stability of linear neutral time-varying differential systems. A brief discussion to the obtained results is given. To the best of our knowledge, the results of this paper are new.

An improved stability criterion for time-delay power systems with electric vehicles and high voltage direct current power links

This paper presents an improved stability criterion for load frequency control (LFC) of time-delay power systems including AC/HVDC transmission links and EVs. By employing a novel refined Jensen-based inequality, an improved stability condition is derived in terms of feasible linear matrix inequalities (LMIs) which allow us to compute the maximal upper bounds of time-delay ensuring stability of the LFC scheme equipped with an embedded controller. Cases studies here are implemented for LFC scheme of a two-area power system, which is interconnected by parallel (AC/HVDC) links, with embedded proportional integral (PI) controller for discharged EVs. The relationships between the parameters of PI controller, supplementary control of HVDC links and delay margins of the LFC scheme are also discussed. As a consequence of facts, the results of delay margins can be used as a guideline to tune PI controller and set-up parameters for HVDC control.

Static output feedback frequency stabilization of time-delay power systems with coordinated electric vehicles state of charge control

In this paper, for the first time, electric vehicles are used for both the primary and secondary frequency controls to support power plants to rapidly suppress fluctuations in the system frequency due to load disturbances. Via networked control and wide-area communication infrastructures, multiple interval time-varying delays exist in the communication channels between the control center, power plant, and an aggregation of electric vehicles. By coordinating batteries’ state of charge control, the behaviors of the vehicle owners and the uncertainties imposed by the changes of the batteries’ state of charge are taken intoconsideration. A power system model incorporating multiple time-varying delays and uncertainties is first proposed. Then, a robust static output feedback frequency controller is designed to guarantee the resulting closed-loop system stable with an H∞ attenuation level. By utilizing a novel integral inequality, namely refined-Jensen inequality, and an improved reciprocally convex combination, the design conditions are formulated in terms of tractable linear matrix inequalities which can be efficiently solved by various computational tools. The effectiveness of the proposed control scheme is verified by extensive simulations.

Robust finite-time consensus tracking algorithm for multirobot systems

This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.

Development of a new versatile computer controlled electrochemical/ESR data acquisition system

A new versatile computer controlled electrochemlcal/ESR data acquisition system has been developed for the Investigation of short-lived radicals with life-times of 20 milliseconds and greater, Different computer programs have been developed to monitor the decay of radicals; over hours or minutes, seconds or milliseconds. Signal averaging and Fourier smoothing is employed in order to improve the signal to noise ratio. Two microcomputers are used to control the system, one home-made computer containing the M6800 chip which controls the magnetic field, and an IBM PC XT which controls the electrochemistry and the data acquisition. The computer programs are written in Fortran and C, and call machine language subroutines, The system functions by having the radical generated by an electrochemical pulse: after or during the pulse the ESR data are collected. Decaying radicals which have half-lives of seconds or greater have their spectra collected in the magnetic field domain, which can be swept as fast as 200 Gauss per second. The decay of the radicals in the millisecond region is monitored by time-resolved ESR: a technique in which data is collected in both the time domain and in the magnetic field domain. Previously, time-resolved ESR has been used (without field modulation) to investigate ultra-short-lived species with life-times in the region of only a few microseconds. The application of the data acquisition system to chemical systems is illustrated. This is the first time a computer controlled system whereby the radical is generated by electrochemical means and subsequently the ESR data collected, has been developed.

Adaptive hierarchical scheduling policy for enterprise grid computing systems

In an enterprise grid computing environments, users have access to multiple resources that may be distributed geographically. Thus, resource allocation and scheduling is a fundamental issue in achieving high performance on enterprise grid computing. Most of current job scheduling systems for enterprise grid computing provide batch queuing support and focused solely on the allocation of processors to jobs. However, since I/O is also a critical resource for many jobs, the allocation of processor and I/O resources must be coordinated to allow the system to operate most effectively. To this end, we present a hierarchical scheduling policy paying special attention to I/O and service-demands of parallel jobs in homogeneous and heterogeneous systems with background workload. The performance of the proposed scheduling policy is studied under various system and workload parameters through simulation. We also compare performance of the proposed policy with a static space–time sharing policy. The results show that the proposed policy performs substantially better than the static space–time sharing policy.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.

Refined Jensen-based inequality approach to stability analysis of time-delay systems

© 2015 The Institution of Engineering and Technology. In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time-delay systems, namely discrete and distributed constant delays systems and interval time-varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 - delay-dependent, and 2 - internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen's inequality, and improved Park's inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario.