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Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma

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Abstract

This paper investigates the problem of stability and robust stabilization of two-dimensional (2-D) continuous–discrete systems in Roesser model. Based on Kalman–Yakubovich–Popov (KYP) lemma, sufficient conditions of stability of the systems are proposed in terms of linear matrix inequalities (LMIs). Moreover, combining generalized KYP lemma with frequency-partitioning idea, the conservativeness of the stability conditions may be further reduced. Robust stabilization using state feedback is studied as well and stabilizing feedback gain matrices are constructed based on the solutions of certain LMIs. In addition, the stability analysis of a class of differential repetitive processes, a special case of 2-D continuous–discrete systems in Roesser model, can adopt the results in this manuscript. Numerical examples are presented to verify the effectiveness of the method.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 11201240 and in part by the Research Fund for the Doctoral Program of Higher Education of China under Grant 20133219110040.

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Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China

    Lanning Wang

  2. School of Science, Nanjing University of Science and Technology, Nanjing, China

    Lanning Wang, Weiqun Wang, Jingbo Gao & Weimin Chen

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  1. Lanning Wang
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  2. Weiqun Wang
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  3. Jingbo Gao
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  4. Weimin Chen
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Correspondence to Lanning Wang.

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Wang, L., Wang, W., Gao, J. et al. Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma. Multidim Syst Sign Process 28, 251–264 (2017). https://doi.org/10.1007/s11045-015-0355-2

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  • DOI: https://doi.org/10.1007/s11045-015-0355-2

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