H∞ control for discrete-time singularly perturbed systems with two Markov processes

This paper discusses the H∞ state feedback control problem for discrete-time Markovian jump singularly perturbed systems whose singularly perturbation parameters belong to another Markov process. Firstly, new mean-square exponential stability condition with H∞ performance for discrete-time singularly perturbed systems with two Markov processes is given in terms of linear matrix inequalities (LMIs) with equality constraints via a novel method. Then, based on the derived stability condition where ε is involved, however, an H∞ controller which is independent of ε is constructed. An effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the H∞ controller solutions. Finally, illustrative examples are presented to show the benefits and validity of the proposed approaches.