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control for discrete-time singular Markovian jump systems based on the novel bounded real lemma

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  • Jianhua Wang
  • Qingling Zhang
  • Xiaoxu Liu

Abstract

This paper considers the H∞ control problem for the discrete-time singular Markovian jump systems with partially unknown transition probabilities. First, a new formulation of the bounded real lemma (BRL) for discrete-time singular Markovian jump systems is given by referencing slack variables technique, which ensures the considered systems to be regular, causal and stochastically stable with given H∞ performance index γ. Then, based on this new BRL, the desired controller gains are also presented by solving a set of strict linear matrix inequalities. A numerical example is provided to show the effectiveness and less conservativeness of the proposed methods.

Suggested Citation

  • Jianhua Wang & Qingling Zhang & Xiaoxu Liu, 2015. "control for discrete-time singular Markovian jump systems based on the novel bounded real lemma," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(1), pages 63-75, January.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:1:p:63-75
    DOI: 10.1080/00207721.2014.948947
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    References listed on IDEAS

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    1. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    2. Leonard Mirman & Olivier Morand & Kevin Reffett, "undated". "A Qualitative Theory of Markovian Equilibrium in Infinite Horizon Economies with Capital," Working Papers 2133376, Department of Economics, W. P. Carey School of Business, Arizona State University.
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