Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach

Chen, Wu‐Hua; Guan, Zhi‐Hong; Lü, Xiaomei

doi:10.1016/j.sysconle.2004.10.005

Cited by 247 publications

(181 citation statements)

References 11 publications

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“…In the above actual systems, there is a phenomenon that the random and time-delay are presented at the same time. In order to accurately describe the dynamic characteristics of the systems, the stochastic time-delay systems are established and have attracted the attention of many researchers [34][35][36][37]. A large variety of important and interesting methods have been proposed for the analysis and design of singular fuzzy systems with time-delay [15,16].…”

Section: Introductionmentioning

confidence: 99%

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

et al. 2014

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This paper considers the H ∞ filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e λt -weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e λt -weighted iISSiM and the H ∞ attenuation level from disturbance to estimation error is below a prescribed scalar. A set of sufficient conditions for the solvability of the H ∞ filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper.

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Section: Introductionmentioning

confidence: 99%

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

et al. 2014

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“…Stability and boundedness are two of the most important topics in the study of SDDEs or SFDEs in modern control theory. Many researchers have done a lot of works for these two topics (see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18]). …”

Section: Introductionmentioning

confidence: 99%

The Almost Sure Asymptotic Stability and Boundedness of Stochastic Functional Differential Equations with Polynomial Growth Condition

Feng

2014

Abstract and Applied Analysis

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Stability and boundedness are two of the most important topics in the study of stochastic functional differential equations (SFDEs). This paper mainly discusses the almost sure asymptotic stability and the boundedness of nonlinear SFDEs satisfying the local Lipschitz condition but not the linear growth condition. Here we assume that the coefficients of SFDEs are polynomial or dominated by polynomial functions. We give sufficient criteria on the almost sure asymptotic stability and the boundedness for this kind of nonlinear SFDEs. Some nontrivial examples are provided to illustrate our results.

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“…The stability and control problem for uncertain stochastic delayed systems has been extensively investigated by a considerable number of researchers (Miyamura and Aihara, 2004;Yan et al, 2009;Zhang et al, 2009;Chen et al, 2005;Yue and Han, 2005;He et al, 2010). Tian et al (2010), dealt with the problem of robust H ∞ control design for nonlinear networked control systems, which are presented in the form of a T-S fuzzy model with a time-varying input delay and the whole variation interval of the delay is divided into two subintervals of equal length, which is different from the existing method.…”

Section: Introductionmentioning

confidence: 99%

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Balasubramaniam¹,

Shanmugam²,

Rakkiyappan³

2012

International Journal of Applied Mathematics and Computer Science

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This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

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Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach

Cited by 247 publications

References 11 publications

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

The Almost Sure Asymptotic Stability and Boundedness of Stochastic Functional Differential Equations with Polynomial Growth Condition

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

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