Delay-dependent – filter design for stochastic time-delay systems

Xia, Jianwei; Xu, Shengyuan; Song, Bo

doi:10.1016/j.sysconle.2007.04.001

Cited by 91 publications

(53 citation statements)

References 20 publications

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“…5 that the range of feasible solutions for Corollary 1 of this paper is wider than the result in [32]. Through this example, we can find that our results can be also used in the case of constant time-delay and the range of feasible solutions is wider than the result of [32].…”

Section: Simulation Examplesmentioning

confidence: 67%

“…In Fig. 5,' o' represents the range of the feasible solutions using Corollary 1 of this paper, and ' * ' represents the range of the feasible solutions using Theorem 2 of [32]. It is clear to see from Fig.…”

Section: Simulation Examplesmentioning

confidence: 94%

“…Example 2 Consider the following stochastic system borrowed from [32]: The delay is assumed asd = 1.1. The disturbance attenuation level is chosen as γ = 0.8.…”

Section: Simulation Examplesmentioning

confidence: 99%

“…Using Corollary 1, the filter that is the special case r = 1ofsystem (5) can be obtained. The parameters of the filter are as follows: Fig.5 shows the range of the feasible solutions for Corollary 1 of this paper and Theorem 2 of [32]. In Fig.…”

Section: Simulation Examplesmentioning

confidence: 99%

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$$H_\infty $$ 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: Simulation Examplesmentioning

confidence: 67%

Section: Simulation Examplesmentioning

confidence: 94%

“…Example 2 Consider the following stochastic system borrowed from [32]: The delay is assumed asd = 1.1. The disturbance attenuation level is chosen as γ = 0.8.…”

Section: Simulation Examplesmentioning

confidence: 99%

Section: Simulation Examplesmentioning

confidence: 99%

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

et al. 2014

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“…Free-weighting matrix method has been applied to analyze the mean-square exponential stability of stochastic time-delay systems with Markovian jumping parameters [51,52]. Based on free-weighting technique, the controller and filter designs of stochastic delayed systems have been discussed in [38,49,53]. By input-output method (see [10] in the deterministic context), Gershon et al have proposed delay-dependent results for delayed systems with stochastic perturbations (i.e.…”

Section: Introductionmentioning

confidence: 99%

Robust exponential stability conditions for retarded systems with Lipschitz nonlinear stochastic perturbations

Chen

Xue

Zheng

et al. 2010

Int. J. Robust Nonlinear Control

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SUMMARYThis 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.

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Robust L₂−L_∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

Jia

2011

Asian Journal of Control

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This paper is devoted to the problem of robust L 2 .L ∞ filtering for a class of stochastic systems with both discrete and distributed time-varying delays. The objective is to design a full-order filter such that the resulting filtering error system is stochastically asymptotically stable with a prescribed L 2 .L ∞ performance satisfied. Delay-dependent sufficient condition for the existence of the filter is obtained in terms of linear matrix inequalities (LMIs). And the filter design method is proposed, while the explicit expression for the desired filter is also given. Numerical examples are included to illustrate the benefit and the effectiveness of the proposed method.

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Delay-dependent – filter design for stochastic time-delay systems

Cited by 91 publications

References 20 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

Robust exponential stability conditions for retarded systems with Lipschitz nonlinear stochastic perturbations

Robust L₂−L_∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

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Delay-dependent – filter design for stochastic time-delay systems

Cited by 91 publications

References 20 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

Robust exponential stability conditions for retarded systems with Lipschitz nonlinear stochastic perturbations

Robust L2−L∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

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Robust L₂−L_∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays