Delay-dependent Robust Exponential Stability Research Articles

New delay-dependent robust exponential stability for uncertain linear systems with multiple non-differentiable time-varying delays and nonlinear perturbations

This paper studies delay-dependent robust stability analysis for uncertain linear systems with constant delay, time-varying delay and nonlinear perturbations. The restriction on the derivative of time-varying delay is removed, which means that the fast time-varying delays are allowed. Combined with Leibniz-Newton formula, integral inequalities, Wirtinger-based integral inequality, Peng-Park’s integral inequality, utilization of zero equation and new Lyapunov-Krasovskii functional have been adopted to study. New delay-dependent robust stability criteria for uncertain time-delay systems are established in terms of linear matrix inequalities (LMIs). Numerical examples and simulation suggest that the results given to illustrate the effectiveness and improvement over some existing methods.

Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

This paper concerns managing the robust exponential stability problem of uncertain Takagi–Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov–Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.

New delay-dependent robust exponential stability for uncertain stochastic systems with multiple delays based on extended reciprocally convex approach

New delay-dependent robust exponential stability for uncertain stochastic systems with multiple delays based on extended reciprocally convex approach

New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing a Lyapunov–Krasovskii functional, and using poincare inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.

Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen–Grossberg neural networks with mixed delays

This paper is devoted to investigating the robust stochastic exponential stability for reaction-diffusion Cohen–Grossberg neural networks (RDCGNNs) with Markovian jumping parameters and mixed delays. The parameter uncertainties are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Some criteria for delay-dependent robust exponential stability of RDCGNNs with Markovian jumping parameters are established in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing Matlab LMI toolbox. Numerical examples are provided to demonstrate the efficiency of the proposed results.

Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Delay Dependent Robust Exponential Stability Criterion for Perturbed and Uncertain Neutral Systems with Time Varying Delays

This paper deals with the issue of robust exponential stability of uncertain neutral system with time varying delay and nonlinear perturbations. Using Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs solved using efficient convex optimization algorithms. Neither model transformation, nor estimating techniques for cross terms, nor free weighting matrices are involved in this work. Numerical examples are considered to show the efficiency of the proposed stability approach.

Robust Exponential Stability of Uncertain Singular Markovian Jump Time-delay Systems

In this paper,the problem of delay-dependent robust exponential stability is investigated for uncertain singular Marko- vian jump systems with time delay.A delay-range-dependent condition is given which ensures that the nominal system is regular,impulse free,and mean-square exponentially stable in terms of linear matrix inequality (LMI) approach.The criterion is also extended to uncertain case.Numerical examples are given to show that the proposed criteria improve the existing results.

Robust Exponential Stability of Uncertain Singular Markovian Jump Time-delay Systems

Abstract In this paper, the problem of delay-dependent robust exponential stability is investigated for uncertain singular Markovian jump systems with time delay. A delay-range-dependent condition is given which ensures that the nominal system is regular, impulse free, and mean-square exponentially stable in terms of linear matrix inequality (LMI) approach. The criterion is also extended to uncertain case. Numerical examples are given to show that the proposed criteria improve the existing results.

ROBUST EXPONENTIAL STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS WITH UNCERTAINTIES AND NONLINEAR PERTURBATIONS

In this paper, the delay-dependent robust exponential mean-square stability analysis problem is considered for a class of uncertain stochastic systems with time-varying delay and nonlinear perturbations. Some sufficient conditions on delay-dependent robust exponential stability in the mean square are established in terms of linear matrix inequalities (LMIs) by exploiting a novel Lyapunov–Krasovskii functional and by making use of zero equations methods. These developed results indicate less conservatism than the existing ones due to the introduction of some free weighting matrices which can be selected properly. The new delay-dependent stability criteria are expressed as a set of LMIs, which can be readily solved by using standard numerical software. Numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed criteria.

Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters

This Letter is concerned with delay-dependent robust exponential mean square stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Time delays here are discrete and distributed time-varying delays. Based on Lyapunov–Krasovskii stability theory, delay-dependent stability conditions are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays

This paper is concerned with the problem of stability analysis for a class of discrete-time recurrent neural networks with time-varying delays. Under a weak assumption on the activation functions and using a new Lyapunov functional, a delay-dependent condition guaranteeing the global exponential stability of the concerned neural network is obtained in terms of a linear matrix inequality. It is shown that this stability condition is less conservative than some previous ones in the literature. When norm-bounded parameter uncertainties appear in a delayed discrete-time recurrent neural network, a delay-dependent robust exponential stability criterion is also presented. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays

This Letter deals with the problem of delay-dependent robust exponential stability in mean square for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-varying delays. Based on Lyapunov–Krasovskii functional and the stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Because of introducing some free-weighting matrices to develop the stability criteria, the proposed stability conditions have less conservatism. Numerical examples are given to illustrate the effectiveness of our results.