Sliding mode control for Itô stochastic systems with Markovian switching

Niu, Yugang; Ho, Daniel W. C.; Wang, Xingyu

doi:10.1016/j.automatica.2007.02.023

Cited by 228 publications

(111 citation statements)

References 15 publications

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“…It is noted that our approach is different from that in the references [25] and [35] in the following perspectives: a) the system structure in [35] does not consider the synchronization problem and the time-delays, i.e., the results in [25] and [35] cannot be directly applied to the system under consideration in this paper; b) the proposed delay-discrete-distribute-dependent conditions in Theorems 1-3 are obtained without resorting to any model transformations and bounding techniques for some cross terms, see for instance [25], thus reducing the conservatism in the derivation of the stability conditions.…”

Section: Remarkmentioning

confidence: 95%

“…Recently, the problem of sliding mode control for a class of nonlinear uncertain stochastic systems with Markovian switching is studied in [34]. More recently, in [35], sliding mode control of nonlinear singular stochastic systems with Markovian switching is proposed. On another research front line, synchronization is a basic motion in nature that has been studied for a long time, ever since the discovery of Christian Huygens in 1665 on the synchronization of two pendulum clocks.…”

Section: Introductionmentioning

confidence: 99%

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A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Karimi

2012

Journal of the Franklin Institute

270

108

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Abstract-In this paper, a sliding-mode approach is proposed for exponential H ∞ synchronization problem of a class of masterslave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent modedependent sliding mode exponential H ∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the  H synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.

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Section: Remarkmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Karimi

2012

Journal of the Franklin Institute

270

108

View full text Add to dashboard Cite

show abstract

“…Stability, stabilization and filtering problems for this kind of system have been addressed in [3,12,17,18,20,27]. Recently, the interconnected Markovian jump systems have received growing attention.…”

Section: Introductionmentioning

confidence: 99%

Decentralized $\mathcal{L}_{2}$ – $\mathcal{L}_{\infty}$ Filtering for Interconnected Markovian Jump Systems with Delays

Fei

Zhang

et al. 2011

Circuits Syst Signal Process

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This paper deals with the problem of decentralized L 2 -L ∞ filtering for a class of interconnected (or large-scale) Markovian jump systems with constant time delays. The purpose is to present delay-dependent conditions for the existence of mode-dependent decentralized filters, which guarantees that the filtering error system is stochastically stable with a prescribed L 2 -L ∞ disturbance attenuation level. Such a purpose is achieved by using a mode-dependent centralized Lyapunov functional together with the so-called Jensen's inequality. The obtained synthesis conditions are expressed in terms of linear matrix inequalities (LMIs), which leads to a convex design method for the concerned filters. An example including numerical and simulation results is provided finally to illustrate the effectiveness of the proposed design method.

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“…Recently, many works have been published on MJLSs (see, for example, [3,20,21,27,28,31,33] and references therein). The literature covers a wide range of problems for MJLSs, including stability analysis and stabilization [8,12,19,26,27], control problems [3,7,15,16,18,23,30], filtering problems [4,17,21,24,25,28,29], and fault detection problems [33]. Among these works, H ∞ type (including H ∞ control, H ∞ filtering, and H ∞ fault detection) problems of MJLSs have been a most active research area in the past decade, and many significant results have been reported (see, for example, [3, 23-25, 28-30, 33]).…”

Section: Introductionmentioning

confidence: 99%

Passivity Analysis and Passification of Markovian Jump Systems

Yao

Zheng

et al. 2010

Circuits Syst Signal Process

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This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov-Krasovskii function and employing the free-weighting matrix 710 Circuits Syst Signal Process (2010) 29: 709-725 technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.

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Sliding mode control for Itô stochastic systems with Markovian switching

Cited by 228 publications

References 15 publications

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

A sliding mode approach to H∞ synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties

Decentralized $\mathcal{L}_{2}$ – $\mathcal{L}_{\infty}$ Filtering for Interconnected Markovian Jump Systems with Delays

Passivity Analysis and Passification of Markovian Jump Systems

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