Reliable Mixed &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$H_\infty $ &lt;/tex-math&gt;&lt;/inline-formula&gt; and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures

Sakthivel, R.; Selvi, S. Chitra; Mathiyalagan, K.; Shi, Peng

doi:10.1109/tcyb.2014.2382563

Cited by 119 publications

(60 citation statements)

References 29 publications

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“…Lemma 2.2 [6] Assume that , M i , and N ai are real matrices with appropriate dimensions and ‡.r k / is a matrix function satisfying ‡ T .r k / ‡ .r k / 6 I , then…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

Sakthivel

Sathishkumar

Mathiyalagan

et al. 2016

Adaptive Control & Signal

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This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time-varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly .Q; S; R/ dissipative. By introducing a novel augmented Lyapunov-Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H 1 performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. n 2 OE0; 1/ stands for the space of n-dimensional square integrable function over OE0; 1/; a positive definite matrix P is denoted by P > 0; I is the unit matrix with appropriate dimension, and means symmetric term in the symmetric matrix.

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“…Lemma 2.2 [6] Assume that , M i , and N ai are real matrices with appropriate dimensions and ‡.r k / is a matrix function satisfying ‡ T .r k / ‡ .r k / 6 I , then…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

Sakthivel

Sathishkumar

Mathiyalagan

et al. 2016

Adaptive Control & Signal

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“…As a consequence, it is not surprising that the past years have witnessed a surge of research interest in the study of nonlinear MJSs by using the fuzzy-model-based approach. For details on research advances about this issue, we refer readers to [3], [20], [28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

Shen

Yan

et al. 2018

IEEE Trans. Fuzzy Syst.

420

120

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Abstract-This paper investigates the finite-time eventtriggered H∞ control problem for Takagi-Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of the network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this work is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closedloop system is finite-time bounded and satisfies a prescribed H∞ performance level, but also the communication burden is reduced. Firstly, a sufficient condition is established for the finitetime bounded H∞ performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the desired controller design method is presented. Finally, two illustrative examples are given to explain the practicability and availability of the designed controller.

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“…In the recent decades, the stability and stabilization analysis for fuzzy systems ( [24]- [30]) especially for Takagi-Sugeno fuzzy model [1] with time delay has been a hot topic (see [2]- [13], [22], [23] and the references therein) and the focus is on how to maximize the tolerance of time delay. All kinds of Lyapunov-Krasovskii functional have been developed to reduce the conservativeness of finding the maximum delay bounds, for example, an augmented Lyapunov-Krasovskii functional is proposed in [5] and an improved Jensen's inequality which is a more general and tighter bounding technology is used to deal with the cross product terms.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Stability and Stabilization Analysis for Continuous-Time Takagi–Sugeno Fuzzy Systems With Time Delay

Wang

Lam

2018

IEEE Trans. Fuzzy Syst.

184

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Abstract-Till now, there are lots of stability and stabilization results about T-S (Takagi-Sugeno) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov-Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T-S fuzzy systems with time delay. Different from the existing results in the literature, the integrand of the Lyapunov-Krasovskii functional in this paper depends not only on the integral variable but also on the membership functions, and thus, the information of the time-derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds. Utilizing the information of the time-derivative of membership, a bunch of controllers are designed according to their sign, and then a switching idea is applied to stabilize the fuzzy system. In the end, two examples are given to illustrate the feasibility and validity of the design and analysis.

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Reliable Mixed <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures

Cited by 119 publications

References 29 publications

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

A New Approach to Stability and Stabilization Analysis for Continuous-Time Takagi–Sugeno Fuzzy Systems With Time Delay

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