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

Jianhua Wang, Qingling Zhang and Xiaoxu Liu

International Journal of Systems Science, 2015, vol. 46, issue 1, 63-75

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.

Date: 2015
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DOI: 10.1080/00207721.2014.948947

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