H∞ CONTROL FOR DISCRETE-TIME SINGULARLY PERTURBED SYSTEMS WITH DISTRIBUTIONAL PROPERTIES

In this paper, the H-infinity control problem for discrete-time singularly perturbed systems (DSPSs) with distributional probabilities is considered. Compared with traditional DSPSs, there are two main differences. The first is the singularly perturbation parameter in our model may be in different intervals instead of a deterministic interval. The second is the occurrence between two DSPSs is random. Via using a stochastic variable satisfying some probabilistic property with known probability distribution, for. the first time, DSPSs switching stochastically are modeled into a new type of DSPSs with stochastic parameter matrices. Mean-square exponential stability condition when; the bound of epsilon can be checked is presented via a new approach. Based on the derived criterion, however, an epsilon-independent switching controller satisfying H-infinity performance is given in terms of linear matrix inequalities (LMIs) with equality constraints. An effective algorithm involving LMIs is suggested to solve the matrix inequalities characterizing the controller solutions. Finally, illustrative examples are presented to show the benefits and the validity of the proposed approaches.