Robust Exponential Stability Criteria Research Articles

Global robust exponential stability of interval BAM neural networks with multiple time-varying delays: A direct method based on system solutions

This paper analyzes global robust exponential stability of interval bidirectional associative memory (BAM) neural networks with multiple time-varying delays, proposes a direct method based on system solutions, and gives sufficient conditions under which interval BAM neural networks have a unique and globally robustly exponentially stable equilibrium point. This method not only avoids the difficult to set up any Lyapunov–Krasovskii functional, but also derives simpler global robust exponential stability criteria. Compared with the data from other literature, the robust exponential stability criteria obtained in this paper have been presented to have more merits theoretically and numerically.

Robust stochastic stability for multi-group coupled models with Markovian switching

As one of the most important topics in control theory, robust stability for the systems plays a key role in many areas of science and industry. This paper discusses the robust stochastic stability a class of multi-group coupled stochastic models with Markovian switching. Based on discrete-time observations in the diffusion part with time-delay, the robust stochastic exponential stability criterion in mean square sense is established in the forms of Lyapunov-type and coefficient-type. An application to the robust stochastic stability for a class of coupled oscillators is proposed.

Stability and control of uncertain ICPT system considering time‐varying delay and stochastic disturbance

SummaryThis paper studies the problem of robust exponential stability for uncertain inductively coupled power transfer (ICPT) system considering time‐varying delay and stochastic disturbance. Firstly, the model of the system is set up via a time domain method. Secondly, based on the Newton‐Leibnitz formula and stability theory, a new stability analysis of the ICPT system with uncertain parameter and time‐varying delay or stochastic disturbance is presented respectively. The proposed approach can be applied for analyzing other similar systems, and the obtained results can be also used for estimating convergence rate and region of stability. Thirdly, based on the Lyapunov‐Krasovskii functional (LKF) approach and the stochastic stability theory, robust exponential stability criteria in the mean square are derived and the relevant controller is designed. The proposed method can further reduce conservatism. Finally, the correctness and effectiveness of the obtained results are verified by an example and simulations indicate that the larger time delay, the slower attenuation. Simultaneously, the uncertain parameter and the stochastic disturbance have a significant influence on the region of stability. In addition, in respect of reducing conservatism, the effectiveness of the proposed method is demonstrated by comparing with other papers. In addition, the designed controller shows better performance for the ICPT system with the parameter uncertainty, the time‐varying delay, and the stochastic disturbance.

Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense

In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.

A New Global Robust Exponential Stability Criterion for H∞ Control of Uncertain Stochastic Neutral-type Neural Networks with Both Timevarying Delays

This paper mainly focuses on a novel H∞ control design to handle the global robust exponential stability problem for uncertain stochastic neutral-type neural networks (USNNNs) with mixed time-varying delays. Here the delays are assumed to be both discrete and distributed, which means that the lower and upper bounds can be derived. Firstly, we draw a control law for stabilized and stability of the neutral-type neural networks (NNNs). Secondly, by employing the Lyapunov-Krasovskii functional(LKF) theory, Jensen’s integral inequality, new required sufficient conditions for the global robust exponential stability of the given neural networks (NNs) are established in terms of delay-dependent linear matrix inequalities (LMIs), which can be easily checked in practice. The conditions obtained are expressed in terms of LMIs whose feasibility can be verified easily by MATLAB LMI control toolbox. Moreover, we have compared our work with previous one in the existing literature and showed that it reduces conservatism. Finally, one numerical example with their simulations is given to validate the effectiveness of our proposed theoretical results.

LMI-based robust exponential stability criterion of impulsive integro-differential equations with uncertain parameters via contraction mapping theory

By formulating a new contraction mapping on a product space, the authors originally employed Banach fixed point theorem to derive the LMI-based robust exponential stability criterion for impulsive BAM neural networks with distributed delays and uncertain parameters. Numerical example illuminates that the new criterion is not worse than the existing results derived by Lyapunov functional method. Hence both the methods and the results of this paper are really novel to a certain extent.

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-range-dependent robust exponential stability criteria for uncertain linear systems with discrete interval and distributed time-varying delays and nonlinear perturbations

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

Robust stability of probabilistic delays fuzzy stochastic p-Laplace dynamic equations

In this paper, the stability of a class of time-delay Takagi-Sugeno (T-S) fuzzy Markovian jumping partial differential equations (PDEs) with p-Laplace and probabilistic time-varying delays is investigated, and the robust exponential stability criterion is obtained by way of some variational methods in Sobolev space W 1 , p (Ω), the Lyapunov functional method and the linear matrix inequalities technique. Moreover, a numerical example shows the effectiveness of the proposed methods due to the large allowable variation range of time delay.

Exponential stability of Markovian jumping stochastic Cohen–Grossberg neural networks with mode-dependent probabilistic time-varying delays and impulses

This paper deals with robust exponential stability of Markovian jumping stochastic Cohen–Grossberg neural networks (MJSCGNNs) with mode-dependent probabilistic time-varying delays, continuously distributed delays and impulsive perturbations. By construction of novel Lyapunov–Krasovskii functional having the triple integral terms, the double integral terms having the positive definite matrices dependent on the system mode and MJSCGNNs system transformation variables, new delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities (LMIs). By establishing a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. Furthermore, a mode-dependent mean square robust exponential stability criterion is derived by constriction of new Lyapunov–Krasovskii functional having modes in the integral terms, linear matrix inequalities and some stochastic analysis techniques. Finally, two numerical examples are provided to show the effectiveness of the proposed methods.

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.

Robust exponential stability of discrete‐time uncertain impulsive neural networks with time‐varying delay

The purpose of this paper is to investigate the robust exponential stability of discrete‐time uncertain impulsive neural networks with time‐varying delay. By using Lyapunov functions together with Razumikhin technique, some new robust exponential stability criteria are presented. The obtained results show that the robust stability can be retained under certain impulsive perturbations for the neural network, which has the robust stability property. The obtained results also show that impulses can robustly stabilize the neural network, which does not have the robust stability property. Some examples, together with their simulations, are also given to show the effectiveness and the advantage of the presented results. It should be noted that the impulsive robust exponential stabilization result for discrete‐time neural network with time‐varying delay is given for the first time. Copyright © 2012 John Wiley & Sons, Ltd.

Robust Exponential Stability of Discrete‐Time Delay Impulsive Systems with Parametric Uncertainties

AbstractThis paper investigates robust exponential stability for discrete‐time delay impulsive systems with parametric uncertainties. The parametric uncertainties in the systems are assumed to be time varying and norm bounded. Using Lyapunov functionals, some robust exponential stability criteria are given. It is shown that the time interval between the nearest two impulses should be small enough, i.e., impulses must act frequently, when the impulses are employed to stabilize the original impulse‐free system that is not robustly stable. Conversely, when the original system without impulses is robustly stable, the time interval between the nearest two impulses should be large enough to let the system with impulsive perturbations retain its stability property. It should be noted that this is the first time that impulsive robust exponential stabilization results are given via Lyapunov functionals for discrete‐time uncertain delay impulsive systems. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.

Robust Exponential Stability Criteria of LPD Systems with Mixed Time‐Varying Delays and Nonlinear Perturbations

This paper investigates the problem of robust exponential stability for linear parameter‐dependent (LPD) systems with discrete and distributed time‐varying delays and nonlinear perturbations. Parameter dependent Lyapunov‐Krasovskii functional, Leibniz‐Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free‐weighting matrices, new delay‐dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Improved global robust exponential stability criteria for interval neural networks with time-varying delays

In this paper, by developing a new approach based on H-matrix theory, some improved sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. Theoretic analysis shows that our results improve and generalize some previously published ones. Finally, some numerical examples are given to show the effectiveness of the obtained results.

Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses

In this paper, the robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses is considered. It is assumed that the considered impulsive neural networks have norm-bounded parametric uncertainties and time-varying delays and the state variables on the impulses may relate to the time-varying delays. By using Lyapunov functions together with Razumikhin technique or with differential inequalities, some new robust exponential stability criteria are provided. Some examples and their simulations, including examples that the stability of which can not be tackled by the existing results, are also presented to illustrate the effectiveness and the advantage of the obtained results.

Robust exponential stability of uncertain impulsive delay difference equations with continuous time

In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.

Robust exponential stability criteria of uncertain stochastic systems with time-varying delays

This article investigates the problem of delay-dependent exponential stability in mean square for continuous-time linear stochastic systems with structured uncertainties and time-varying delays. By applying descriptor model transformation of the systems, a new type of Lyapunov–Krasovskii functional is constructed, and by introducing some free weighting matrices, some new delay-dependent and delay-independent stability criteria are derived respectively in terms of an LMI algorithm. The new stability criteria are less conservative than existing results. Numerical examples demonstrate that the new criteria are effective and are an improvement over existing results.

Robust Exponential Stability Criteria for T–S Fuzzy Stochastic Delayed Neural Networks of Neutral Type

This paper is concerned with the problem of robust exponential stability for T–S fuzzy stochastic neural networks of neutral type. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, new delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) which can be checked easily by the LMI Control Toolbox in MATLAB. Finally, numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.