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The objective of this paper is to propose a generalized approach to stabilization of systems which are composed of linear time-delay subsystems coupled by linear time-varying interconnections. The proposed algorithms, which are formulated within the convex optimization framework, provide decentralized solutions to the problem of delay-dependent asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness and disturbance attenuation. Then a decentralized structure of dissipative state-feedback controllers is designed to render the closed-loop interconnected system delay-dependent asymptotically stable with strict dissipativity. Numerical examples are presented to illustrate the applicability of the design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

In this paper, the problem of delay-dependent robust filtering of linear discrete-time singular systems with time-varying delays and polytopic uncertainties is thoroughly investigated. We employ a linear regular filter to ensure its practical realizability. We establish the filter admissibility condition and then using a novel augmented Lyapunov–Krasovskii functional, we develop a new delay-dependent filtering criteria without relying on overbounding for both the nominal and the uncertain cases. We solve the filter design problem based on H∞ -performance criteria. Seeking computational convenience, all the developed results are cast in the form of strict linear matrix inequalities and a numerical example is presented. [ABSTRACT FROM PUBLISHER]

This paper establishes improved global exponential stability method for a class of discrete-time recurrent neural networks with interval time-varying delays and norm-bounded time-varying parameter uncertainties. The method is robust and delay range dependent. It is derived based on a new Lyapunov–Krasovskii functional constructed to exhibit the delay-dependent dynamics and to compensate for the enlarged time span. The developed stability method eliminates the need for over bounding and utilizes smaller number of linear matrix inequality (LMI) decision variables. New and less conservative solutions to the global stability problem are provided in terms of feasibility testing of new parameterized LMIs. Numerical examples are presented to illustrate the effectiveness of the developed technique. [ABSTRACT FROM PUBLISHER]

In this article, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov-function method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities to guarantee the desired ℓ1-performance. A robust state-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example. [ABSTRACT FROM AUTHOR]

This paper develops a decentralized approach to the robust stability and stabilization problems of class of non-linear interconnected discrete-time systems with arbitrary switched rules. This class of interconnected systems consists of coupled nominally linear subsystems with unknown-but-bounded state delay. We showed that multi-controller switched schemes provide an effective and powerful mechanism to cope with highly complex systems with large uncertainties. We developed a delay-dependent decentralized structure that guarantees asymptotic stability with local disturbance attenuation on the subsystem level. Then we constructed decentralized switched control schemes based on state feedback and dynamic output feedback to ensure stabilizability of the global system with ℓ2-performance bound. The theoretical developments are demonstrated by numerical simulation of a multi-reach water pollution control problem. [ABSTRACT FROM PUBLISHER]

In this paper, the problem of quantized feedback stabilization is approached from a generalized setting by designing a decentralized ℋ∞ feedback control for a class of linear interconnected continuous-time systems with unknown-but-bounded couplings and interval delays and where the quantizer has arbitrary form that satisfies a quadratic inequality constraint. An LMI-based method using a decentralized quantized output-feedback controller is designed at the subsystem level to render the closed-loop system delay-dependent asymptotically stable with guaranteed γ-level. It is established that this setting encompasses several special cases of interest including interconnected delay-free systems, single time-delay systems and single systems. We illustrate the theoretical developments by numerical simulations. [ABSTRACT FROM PUBLISHER]

Abstract: This paper develops new robust delay-dependent filter design for a class of linear systems with time-varying delays and convex-bounded parameter uncertainties. The design procedure hinges upon the constructive use of an appropriate Lyapunov functional plus a free-weighting matrices in order to exhibit the delay-dependent dynamics. The developed approach utilizes smaller number of LMI decision variables thereby leading to less conservative solutions to the delay-dependent stability and filtering problems. Subsequently, linear matrix inequalities (LMIs)-based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level . All the developed results are tested on representative examples. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the problem of global exponential stability analysis for a class of bidirectional associative memory (BAM) neural networks with interval time-delays. Improved exponential stability condition is derived by employing new Lyapunov–Krasovskii functional and the integral inequality. Several special cases of interest are derived. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs). The developed results are shown to be less conservative than previous published ones in the literature. Finally, simulations of two numerical examples are provided to demonstrate the efficacy of our approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples. [Copyright &y& Elsevier]

Abstract: This paper develops a decentralized approach to the robust stability and stabilization problems of a class of interconnected continuous-time switched systems with cone-bounded uncertainties and nonlinearities. This class consists of coupled nominally linear subsystems with unknown-but-bounded time-varying state-delay. We showed that multi-controller switched schemes provide an effective and powerful mechanism to cope with highly complex systems with large. We developed a delay-dependent decentralized structure that guarantees global asymptotic stability with local disturbance attenuation on the subsystem level. Then, we constructed decentralized switched control schemes based on state-feedback to ensure stabilizability of the global system with -performance bound. The theoretical developments are illustrated on a representative example. [Copyright &y& Elsevier]

In this paper, a new approach to decentralized feedback stabilization of a class of non-linear interconnected discrete-time systems is proposed. This class of systems has unknown-but-bounded state-delay and uncertain non-linear perturbations satisfying quadratic constraints. The proposed approach is formulated within the framework of convex optimization over linear matrix inequalities. The developed methods employ linear state feedback and linear output feedback structure involving local Luenberger-type observer. All the closed-loop systems guarantee global delay-dependent stability condition which is derived in terms of subsystem variables. Incorporating feedback gain perturbations, new resilient decentralized feedback schemes are developed. All the developed results are tested on a representative example. [ABSTRACT FROM PUBLISHER]

In this paper, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov–Krasovskii functional method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities (LMIs) to guarantee that the desired ℓ1-performance is achieved. A robust dynamic output-feedback controller with arbitrary order is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example. [ABSTRACT FROM PUBLISHER]

Abstract: This paper establishes new robust delay-dependent stability and stabilization methods for a class of nonlinear discrete-time systems with time-varying delays. The parameter uncertainties are convex-bounded and the unknown nonlinearities are time-varying perturbations satisfying Lipschitz conditions in the state and delayed-state. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics and compensate for the enlarged time-span. The developed methods for stability and stabilization eliminate the need for over bounding and utilize smaller number of LMI decision variables. New and less conservative solutions to the stability and stabilization problems of nonlinear discrete-time system are provided in terms of feasibility-testing of new parametrized linear matrix inequalities (LMIs). Robust feedback stabilization methods are provided based on state-measurements and by using observer-based output feedback so as to guarantee that the corresponding closed-loop system enjoys the delay-dependent robust stability with an gain smaller that a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of robust global exponential stability analysis for uncertain neural networks with interval time-varying delays. The time-delay pattern is quite general and including fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. The activation functions are monotone nondecreasing with known lower and upper bounds. Novel stability criteria are developed by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs)-based conditions. The developed stability results are less conservative than previous published ones in the literature, which is illustrated by a representative numerical example. [Copyright &y& Elsevier]

This paper develops novel robust stability and feedback stabilization criteria with guaranteed performance for a class of linear continuous time-delay systems with polytopic uncertainties. The time-varying delay function is unknown and differentiable within bounded interval and the input delay is constant. The criteria is derived based on the constructive use of a new Lyapunov–Krasovskii functional together with the integral inequality. The developed stability condition is expressed in terms of linear matrix inequality that manipulates fewer decision variables and requires reduced computational load. Through a comparison with other existing stability methods, it is established that the developed method retains some useful terms that are frequently dropped out and does not employ any free-weighting matrices to avoid redundancy. A state-feedback stabilizing controller is designed to ensure that the closed loop is robustly stable with guaranteed performance. Representative examples are simulated to illustrate the developed results. [ABSTRACT FROM PUBLISHER]

Abstract: The problem of designing a globally exponentially convergent state estimator for a class of delayed neural networks is investigated in this paper. The time-delay pattern is quite general and including fast time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. A linear estimator of Luenberger-type is developed and by properly constructing a new Lyapunov–Krasovskii functional coupled with the integral inequality, the global exponential stability conditions of the error system are derived. The unknown gain matrix is determined by solving a delay-dependent linear matrix inequality. The developed results are shown to be less conservative than previously published ones in the literature, which is illustrated by a representative numerical example. [Copyright &y& Elsevier]

Abstract: The generalized control problem for a class of linear discrete-time switched systems with constant unknown delays is investigated. New linear matrix inequalities (LMIs) characterization based on switched Lyapunov–Krasovskii functional are established to guarantee the asymptotic stability and generalized performance. Design of generalized state feedback and dynamic output-feedback controllers are developed. A numerical example is worked out in detail to illustrate the theoretical developments. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the delay-dependent performance analysis and control synthesis of a class of linear discrete-time hybrid systems with time-varying delays. We employ hybrid Lyapunov–Krasovskii functionals to establish the desired results under arbitrary switching. A generalized approach is adopted and new parameterized linear matrix inequalities (LMIs) characterization are developed to guarantee the delay-dependent asymptotic stability. Design of generalized state feedback and dynamic output-feedback controllers are subsequently constructed. A numerical example is solved in detail to illustrate the theoretical developments. [Copyright &y& Elsevier]

Abstract: A class of non-linear discrete-time systems with state-delay is considered. We develop an LMI-based analysis and design procedures to check primarily into the robust stability of discrete-time systems with state-delay and bounded non-linearities. Then we address the robust stabilization using nominal and resilient feedback designs. In both cases the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. Seeking computational convenience, all the developed results are cast in the format of linear matrix inequalities (LMIs) and several numerical examples are presented throughout the paper to illustrate the feasibility of the theoretical developments. [Copyright &y& Elsevier]

Abstract: This paper focuses on the controller resilience and performance deterioration issues due to inaccuracies in controller implementation. It addresses the problem of resilient adaptive control problem for a class of discrete-time state-delay systems and norm-bounded uncertainties against controller gain variations. Adaptive control schemes are constructed for the case of known gain perturbation bounds and then extended to accommodate unknown norm-bounded perturbations. Necessary and sufficient conditions for delay-independent asymptotic stability are established. An expanded state-space system called the “Compact Form” is established to derive delay-dependent criteria for stability and adaptive stabilization schemes. All the developed results are conveniently expressed in linear matrix inequalities format. A detailed simulation result is presented to demonstrate the developed theory. [Copyright &y& Elsevier]

A class of linear, uncertain discrete-time systems with state delay is considered. We develop an linear matrix inequality (LMI)-based analysis and redesign procedures for improved robust stability of discrete-time systems with state delay and bounded nonlinearities. Then, we address the robust stabilization using nominal and resilient feedback designs. In both cases, the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. Seeking computational convenience, all the developed results are cast in the format of LMIs and several numerical examples are presented throughout the paper. [ABSTRACT FROM PUBLISHER]

This paper develops new results to the problem of simultaneous feedback stabilization using static output feedback (SOF) control for a finite collection of linear dynamical systems with unknown state delay. We establish tractable synthesis conditions for nominal SOF controllers and subsequently extend the results to resilient SOF to cope with possible additive controller gain perturbations. In both cases, the design of SOF controllers is based on guaranteed cost and ℋ∞ approaches. Previous related results are recovered and all the developed results are conveniently cast in the format of linear matrix inequalities. A numerical example is presented. [ABSTRACT FROM PUBLISHER]