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Robust H 2 Control for Descriptor System Based on New Bounded Real Lemma

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Abstract

This paper is concerned with the problem of robust H 2 control for an uncertain continuous descriptor system based on a new bounded real lemma. Our purpose is to present sufficient and necessary conditions such that the uncertain descriptor system is regular, impulse free, and stable for all admissible uncertainties, while the H 2 norm of the descriptor system is less than a given positive number γ. To this end, a new bounded real lemma for the robust H 2 control problem is first derived in terms of a strict linear matrix inequality (LMI). Secondly, based on this bounded real lemma, a design method of state feedback control is developed to guarantee robust H 2 performance. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou, 310018, PR China

    Renquan Lu, Wei Du, Jianzhong Wang & Anke Xue

Authors
  1. Renquan Lu
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  2. Wei Du
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  3. Jianzhong Wang
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  4. Anke Xue
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Corresponding author

Correspondence to Renquan Lu.

Additional information

This work is supported by the National Nature Science Foundation of China (NNSFC: 60604003, 600421002 and 60874058) and the National Key Basic Research Program (NKBRP:2007CB714000).

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Lu, R., Du, W., Wang, J. et al. Robust H 2 Control for Descriptor System Based on New Bounded Real Lemma. Circuits Syst Signal Process 28, 869–882 (2009). https://doi.org/10.1007/s00034-009-9133-4

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  • DOI: https://doi.org/10.1007/s00034-009-9133-4

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