Robust Exponential Stability Research Articles

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 of nonlinear impulsive switched systems with time-varying delays

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results.

Robust stability analysis of interval fuzzy Cohen–Grossberg neural networks with piecewise constant argument of generalized type

In this paper, existence and uniqueness of the solution of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument are discussed. Based on the comparison principle, it presents new theoretical results on the global robust exponential stability of interval fuzzy Cohen-Grossberg networks with piecewise constant argument. As a special case, the corresponding results of interval fuzzy recurrent neural networks with piecewise constant argument are derived. Three examples are given for illustrating validity of the obtained 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.

Stochastic exponential robust stability of interval neural networks with reaction–diffusion terms and mixed delays

The stochastic exponential robust stability is considered for a class of delayed neural networks with reaction–diffusion terms and Markov jumping parameters in this paper. It is assumed that the uncertain weight matrices belong to the given interval matrices. Some sufficient conditions for the stochastic exponential robust stability of the system are established by applying vector Lyapunov function method and M-matrix theory. The obtained results involving the effect of reaction–diffusion improve the existing conditions. Finally, two examples with numerical simulations are given to illustrate the obtained results.

Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay

This paper studies the problem of robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay. The state variables on the impulses are assumed dependent on the present state variables as well as delayed state variables. Based on the Razumikhin techniques and Lyapunov functions, some robust mean-square exponential stability criteria are derived in terms of linear matrix inequalities. The results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows. Furthermore, the robust delayed-state-feedback controllers that mean-square exponentially stabilize the uncertain impulsive stochastic systems are proposed. Finally, several numerical examples are given to show the effectiveness of the results.

New stability criteria for neutral-type Cohen–Grossberg neural networks with discrete and distributed delays

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results.

Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.

Robust H∞ filtering for switched stochastic systems under asynchronous switching

This paper investigates the problem of robust H∞ filtering for switched stochastic systems under asynchronous switching. The so-called asynchronous switching means that the switching between the filters and system modes is asynchronous. The aim is to design a filter ensuring robust exponential mean square stability and a prescribed H∞ performance level for the filtering error systems. Based on the average dwell time approach and piecewise Lyapunov functional technique, sufficient conditions for the existence of the robust H∞ filter are derived, and the proposed filter can be obtained by solving a set of LMIs(linear matrix inequalities). Finally, a numerical example is given to show the effectiveness of the proposed approach.

Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks

This Letter addresses the stability analysis problem for a class of uncertain discrete-time stochastic fuzzy neural networks (DSFNNs) with time-varying delays. By constructing a new Lyapunov–Krasovskii functional combined with the free weighting matrix technique, a new set of delay-dependent sufficient conditions for the robust exponential stability of the considered DSFNNs is established in terms of Linear Matrix Inequalities (LMIs). Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained theory.

Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov‐Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay‐dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Robust Exponential Stability for LPD Discrete‐Time System with Interval Time‐Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear‐parameter dependent (LPD) discrete‐time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time‐varying delay are available. The uncertainty under consideration is norm‐bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov‐Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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.

LMI‐Based Approach for Exponential Robust Stability of High‐Order Hopfield Neural Networks with Time‐Varying Delays

This paper studies the problems of global exponential robust stability of high‐order hopfield neural networks with time‐varying delays. By employing a new Lyapunov‐Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high‐order neural networks are established, which are easily verifiable and have a wider adaptive.

Exponential stability analysis for the switched stochastic Hopfield neural networks with time-varying delays

In this paper, the robust exponential stability analysis is investigated for a class of switched stochastic Hopfield neural systems with parameter uncertainties and stochastic perturbations. The parameter uncertainties are assumed to be norm bounded. Firstly, based on Lyapunov-Krasovskii functional and linear matrix inequality (LMI) tools, by means of multiple Lyapunov function techniques, a delay-dependent sufficient condition is derived for the switched stochastic neural networks with time-varying delays under an appropriate switching law. Secondly, the sufficient criteria are given to guarantee the uncertain switched stochastic Hopfield neural systems to be mean-square exponentially stable for all admissible parametric uncertainties. Finally, numerical examples are provided to illustrate the effectiveness of the proposed theory.

Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

A class of interval neural networks with time‐varying delays and distributed delays is investigated. By employing H‐matrix and M‐matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical 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.

Leader–follower type relative position keeping in satellite formation flying via robust exponential stabilization

SUMMARYSatellite formation flying is an essential technology in both the current and the future aerospace industry. Conducting a fast and safe flying formation between satellites is always a key requirement for successful mission accomplishment. This paper addresses a leader–follower type relative position keeping in satellite formation flying via a novel robust exponential stabilization. This paper establishes an exponentially convergent relative position keeping taking account of various external disturbances that cannot be modeled into current formation dynamics, along with a set of time‐varying model parameters and measurement noises. The condition for an exponential convergence is established by decomposing the positive definite matrix used in Lyapunov function candidate into several element‐wise submatrices. Through numerical simulations, the effectiveness of the proposed method is illustrated. Copyright © 2011 John Wiley & Sons, Ltd.

Exponential l2 − l∞ filtering for discrete‐time switched systems under a new framework

SUMMARYIn this paper, a robust exponential l2 − l∞ filtering problem is addressed for discrete‐time switched systems with polytopic uncertainties. The purpose of robust exponential l2 − l∞ filtering is to design a filter such that the resulting filtering error system is robustly exponentially stable with a decay rate and a prescribed exponential l2 − l∞ performance index. The robust exponential l2 − l∞ filtering problem is solved via an average dwell time approach. Sufficient conditions in terms of strict LMI are derived for checking the robust exponential stability of a filter. An explicit expression for the desired robust exponential filter is also given. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

Robust exponential stability of impulsive switched systems with switching delays: A Razumikhin approach

In this paper, we focus on the robust exponential stability of a class of uncertain nonlinear impulsive switched systems with switching delays. We introduce a novel type of piecewise Lyapunov–Razumikhin functions. Such functions can efficiently eliminate the impulsive and switching jump of adjacent Lyapunov functions at impulsive switching instants. By Razumikhin technique, the delay-independent criteria of exponential stability are established on the minimum dwell time. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained theoretical results.