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

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.