Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.

Functional observer-based fault detection of time-delay systems via an LMI approach

This paper presents a novel residual generator that uses minimum-order functional observers to trigger actuator and component faults in time-delay systems. We first present a fault detection scheme and derive existence conditions of the residual generator and functional observer. The observer and residual parameters are then systematically determined via solving some coupled generalized Sylvester matrix equations. To deal with the time-delay issue, a stabilizability condition expressed in terms of linear matrix inequality (LMI) is derived to ensure the time-delay observer error system converges to zero with a prescribed convergence rate. Our design approach has the advantage that the designed fault detection scheme has lower order than existing results in the literature. Two numerical examples are given to illustrate the effectiveness of our results.

An LMI-based functional estimation scheme of large-scale time-delay systems with strong interconnections

In this paper, the problem of distributed functional state observer design for a class of large-scale interconnected systems in the presence of heterogeneous time-varying delays in the interconnections and the local state vectors is considered. The resulting observer scheme is suitable for strongly coupled subsystems with multiple time-varying delays, and is shown to give better results for systems with very strong interconnections while only some mild existence conditions are imposed. A set of existence conditions are derived along with a computationally simple observer constructive procedure. Based on the Lyapunov-Krasovskii functional method (LKF) in the framework of linear matrix inequalities (LMIs), delay-dependent conditions are derived to obtain the observer parameters ensuring the exponential convergence of the observer error dynamics. The effectiveness of the obtained results is illustrated and tested through a numerical example of a three-area interconnected system.

Characteristics evaluation of an LMI-synthesis H∞ controller for a superconducting magnetic energy systems applied in power systems

© 2015 IEEE.This paper presents an H« controller synthesised based on linear matrix inequalities (LMI) for a current source converter based superconducting magnetic energy systems (SMESs) connected to a node of power systems where the regulation of grid current has considered as a control objective. To facilitate the control design, the system is represented in terms of state space realization with uncertainties. The control design involves selecting proper weighting functions and performing LMI-synthesis. The controller order is reduced by Henkel-norm method. Simulations are carried out to evaluate the characteristics of the controller under parametric uncertainties. It is found out that the proposed controller is inherently stable, possesses significantly small tracking error, and preserves robust performance for the SMES.

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.

Exponential stabilization for state and input delay systems via output feedback

This paper considers the exponential stabilization problem via static and dynamic output feedback controllers of linear systems with a time delay in both the state and input. By using a change of the state variable and combining with the Lyapunov-Krasovskii method, new sufficient conditions for exponential stabilization via static and dynamic output feedback controllers are proposed. The conditions are expressed in terms of matrix inequalities but with only one parameter needs to be tuned and therefore can be efficiently solved by incorporating an one-dimensional search method into the Matlab’s LMI toolbox. Two numerical examples are provided to illustrate the obtained results.

Observer-based controller design of time-delay systems with an interval time-varying delay

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov–Krasovskii functionals and utilizing the Newton–Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

Full-order observer design for nonlinear complex large-scale systems with unknown time-varying delayed interactions

This article is concerned with the problem of state observer for complex large-scale systems with unknown time-varying delayed interactions. The class of large-scale interconnected systems under consideration is subjected to interval time-varying delays and nonlinear perturbations. By introducing a set of argumented Lyapunov–Krasovskii functionals and using a new bounding estimation technique, novel delay-dependent conditions for existence of state observers with guaranteed exponential stability are derived in terms of linear matrix inequalities (LMIs). In our design approach, the set of full-order Luenberger-type state observers are systematically derived via the use of an efficient LMI-based algorithm. Numerical examples are given to illustrate the effectiveness of the result

Is the adiposity rebound a rebound in adiposity?

OBJECTIVE: Early adiposity rebound ([AR], when body mass index [BMI] rises after reaching a nadir) strongly predicts later obesity. We investigated whether the upswing in BMI at AR is accompanied by an increase in body fat. DESIGN: Community-based cohort study. SUBJECTS: A total of 299 first-born children (49% male). Measurements. Six-monthly anthropometry and bioelectrical impedance, 4-6.5 years; lean and fat mass index (kg/m(2)) for direct comparison with BMI. Supplementary (0-2 years) weight and length measures (needed for growth curve modelling) were drawn from subjects' child health records. METHODS: AR was estimated from individually modelled BMI curves from birth to 6.5 years. Two main analyses were performed: 1) cross-sectional comparisons of BMI, fat mass index (FMI), lean mass index (LMI) and percent body fat in children with early (<5 years) and later (>5 years) rebound; and 2) investigation of linear trends in BMI, FMI, LMI and percent body fat before and after AR. Results. The 81 children (27%) experiencing early AR had higher BMI, FMI, LMI and percent fat at 6.5 years. Overall, FMI decreased steeply pre-AR, at -0.56 (0.02) kg/m(2) per year (mean [Standard Error]), then flattened post-AR to 0.07 (0.05) kg/m(2) per year. In contrast, LMI increased pre-AR (0.34 [0.01]) and steepened post-AR (0.47 [0.03] kg/m(2) per year). CONCLUSION: The 'adiposity rebound' is characterised by increasing lean mass index, coupled with cessation of the decline in fat mass index. Understanding what controls the dynamics of childhood body composition and mechanisms that delay AR could help prevent obesity.

Dharma and grief: secularisation of a sacred emotion

The presentation begins with the moving scene of Va¯lmi¯ki's grief over the bereavement of the survivor of the two birds in amorous union as one of them is pierced by a hunter's arrow. After considering Abhinavagupta's doubt about the genuineness of Va¯lmi¯ki's grief, the paper moves to Maha¯bha¯rata as the women from the warring clans bear witness to the horrendous carnage ensuing from the battle, and the constant rebuke that Yudhisthira, head of the Pa¯ndava clan, faces from Draupadi¯ for wandering the earth without finding a stable foundation for Dharma or grounding it in firm absolutes. We liken Yudhisthira to Mahatma Gandhi facing the near-collapse of the Indian subcontinent as it was being rent apart with communal violence on the eve of its Independence. But we also compare Yudhisthira with Hamlet, the tragic grief-ridden character, who is equally bewildered and confused by the array of emotions and sensations that overwhelm his lingering body upon news of the death of and ghostly encounter with his murdered father. With this as the context, we take the occasion to explore recent thinking on the 'hard emotions', in particular, grief, sorrow and mourning, and link the challenging inner and social condition to the calling of Dharma (righteous law, normatively worthy action). Drawing from some comparative work (academic and personal) in the study of grief, mourning and empathy, we shall discuss the treatment of this tragic pathos in classical Indic literature and modern-day psychotherapy. We shall demonstrate, despite being secularised, these emotions continue to serve as the sites of imagination at a much more personal and inter-personal level that are not antithetical to a Dharmic (sacred) quest despite their haunting presence even when 'the four walls collapse around one in the intensity of duhkha (suffering, sorrow)' (Tagore).

Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Passivity analysis of memristor-based complex-valued neural networks with time-varying delays

In this paper, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov–Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

Observer design for one-sided Lipschitz discrete-time systems subject to delays and unknown inputs

In this paper, we address the problem of observer design for a class of nonlinear discrete-time systems in the presence of delays and unknown inputs. The nonlinearities studied in this work satisfy the one-sided Lipschitz and quadratically inner-bounded conditions which are more general than the traditional Lipschitz conditions. Both H∞ observer design and asymptotic observer design with reduced-order are considered. The designs are novel compared to other relevant nonlinear observer designs subject to time delays and disturbances in the literature. In order to deal with the time-delay issue as well as the bilinear terms which usually appear in the problem of designing observers for discrete-time systems, several mathematical techniques are utilized to deduce observer synthesis conditions in the linear matrix inequalities form. A numerical example is given to demonstrate the effectiveness and high performance of our results.