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\(H_\infty \) Control for Lur’e Singular Systems with Time Delays

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Abstract

This paper considers the \(H_{\infty }\) control problem for Lur’e singular systems with time delays. By using Lyapunov stability theory, sufficient conditions for the system to be exponentially stable and satisfy the performance index of \(H_{\infty }\) are obtained; these conditions are based on the linear matrix inequality method. Then the design of a state feedback controller is given, by applying a more clever approach for a nonlinear matrix with a special format to convert it into the sum of several linear matrices, such that the closed-loop system is also exponentially stable. Finally, numerical examples illustrate the effectiveness of the proposed method and its advantages over existing approaches.

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The data supporting the conclusions of this article is included within the article.

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Author notes

  1. Juan Zhou and HuiLing Lai are co-first authors and contributed equally to this study.

Authors and Affiliations

  1. College of Science, Northeastern University, Shengyang, 110004, Liaoning, People’s Republic of China

    Juan Zhou & HuiLing Lai

  2. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, 110034, Liaoning, People’s Republic of China

    Bo Men

Authors
  1. Juan Zhou
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  2. HuiLing Lai
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  3. Bo Men
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Correspondence to HuiLing Lai.

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Zhou, J., Lai, H. & Men, B. \(H_\infty \) Control for Lur’e Singular Systems with Time Delays. Circuits Syst Signal Process 41, 1367–1388 (2022). https://doi.org/10.1007/s00034-021-01844-0

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  • DOI: https://doi.org/10.1007/s00034-021-01844-0

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