Robust exponential stability and stabilizability of linear parameter dependent systems with delays

This paper discusses the problem of robust delay-dependent exponential stability for a class of uncertain stochastic systems with time-varying delay. The uncertainty is assumed to be of norm-bounded form. A less conservative robust exponential stability condition is derived by using a new Lyapunov–Krasovskii functional and a free-weighting matrix method in terms of linear matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the proposed method.

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.

In this paper, we consider the problems of robust stability and stabilization of Lurpsilae control systems with time-varying delay. Firstly, by making use of an integral inequality, some delay-dependent robust stability conditions of the system are presented. Then, a sufficient stabilization criterion is established in the terms of linear matrix inequality (LMI), based on the above stability condition and matrix decomposition technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.

Focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time-varying delays. The uncertainties are assumed to be continuous time-varying, nonlinear, and norm bounded. Sufficient conditions for robust exponential stability are given for both single and multiple delays cases.

The robust exponential stability problem for a class of uncertain impulsive stochastic neural networks of neutral-type with Markovian parameters and mixed time-varying delays is investigated. By constructing a proper exponential-type Lyapunov-Krasovskii functional and employing Jensen integral inequality, free-weight matrix method, some novel delay-dependent stability criteria that ensure the robust exponential stability in mean square of the trivial solution of the considered networks are established in the form of linear matrix inequalities (LMIs). The proposed results do not require the derivatives of discrete and distributed time-varying delays to be 0 or smaller than 1. Moreover, the main contribution of the proposed approach compared with related methods lies in the use of three types of impulses. Finally, two numerical examples are worked out to verify the effectiveness and less conservativeness of our theoretical results over existing literature.

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.

Based on the stochastic Fubini theorem, an average Lyapunov functional with regard to spatial variables is constructed, by using Ito formula; the problem of robust exponential stability for a class of linear stochastic system with distributed parameter is investigated. The sufficient conditions for robust exponential stability and almost surely exponential stability are obtained. The corresponding results are also generalized to semi-linear systems.

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and time-varying delays is investigated. On the assumption that each isolated subsystem of the interconnected system can be exponentially stabilized and the corresponding Lyapunov functions are available, using M-matrix property, the differential inequalities with time-varying delays are constructed. By the stability analysis of the differential inequalities, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems (SIS) under arbitrary switching are obtained. The proposed method, which neither requires the individual subsystems to share a common Lyapunov function (CLF), nor needs to know the values of individual Lyapunov functions at each switching time, would provide a new mentality for studying stability of arbitrary switching. In addition, by resorting to average dwell time approach, conditions for guaranteeing the robust exponential stability of SIS under constrained switching are derived. The proposed criteria are explicit, and they are convenient for practical applications. Finally, two numerical examples are given to illustrate the validity and correctness of the proposed theories.

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

<p>In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.</p>

The problem of robust stability and stabilization of stochastic large-scale delay systems has been investigated in recent years. However, the robust exponential stability and stabilization has not been considered. The purpose of this paper is to present delay-dependent criteria for robust decentralized exponential stabilization of the complex systems. The obtained results are based on algebraic Riccati equations and may be extended by using the widely-used LMI techniques.

This paper investigates robust mean-square exponential stability of a class of uncertain stochastic state-delayed systems with Lipschitz nonlinear stochastic perturbation. Based on Lyapunov–Krasovskii functional (LKF) method and free-weighting matrix technique, some new delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs). In order to reduce the conservatism, (1) the delay is divided into several segments, i.e. the delay decomposition method is applied; (2) cross terms estimation is avoided; (3) some information of the cross terms relationships which has not been involved in Reference (IET Control Theory Appl. 2008; 2(11):966–973) is considered. Moreover, from the mathematical point of view, the results obtained by free-weighting matrix technique can be equivalently re-formulated by simpler ones without involving any additional free matrix variables. The effectiveness of the method is demonstrated by numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.

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.

Stability, [formula omitted]-gain and control synthesis for positive switched systems with time-varying delay

This paper mainly concerns with the analysis and design for a class of nonlinear networked control systems (NCSs), which can be represented by a T-S fuzzy model with interval time-varying network delay. By using the convexity of the matrix function, the conservatism caused by enlarging? (t) to ?M can be avoided. The controller parameters that guarantee the asymptotical stability and the performance of the closed-loop system are obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness of the proposed method.