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Delay-Dependent \(H_{\infty }\) Control for Singular Time-Varying Delay Systems with Markovian Jumping Parameters

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Abstract

This paper is concerned with the delay-dependent \(H_{\infty }\) control problem for uncertain singular time-varying delay systems with Markovian jumping parameters. First of all, a new Lyapunov–Krasovskii functional is established to develop the new bounded real lemma (BRL). Sufficient condition is given in terms of linear matrix inequalities (LMIs), which guarantees the system to be stochastically admissible with given \(H_{\infty }\) performance index \(\gamma \). We employ delay decomposition approach and improved Wirtinger inequality to reduce the conservatism. Secondly, based on this BRL, the explicit expression of the desired feedback controller gain is obtained by solving a set of strict LMIs. And the robust \(H_{\infty }\) controller for uncertain systems is also presented. Finally, some numerical examples are provided to illustrate the effectiveness and less conservativeness of the proposed methods.

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  1. School of Science, Northeastern University, Shenyang, 110004, China

    Liping Bai & Juan Zhou

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  1. Liping Bai
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  2. Juan Zhou
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Bai, L., Zhou, J. Delay-Dependent \(H_{\infty }\) Control for Singular Time-Varying Delay Systems with Markovian Jumping Parameters. Circuits Syst Signal Process 41, 6709–6732 (2022). https://doi.org/10.1007/s00034-022-02074-8

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  • DOI: https://doi.org/10.1007/s00034-022-02074-8

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