Robust stability and robust H2 performance of discrete‐time Markovian jump linear systems with uncertain transition probabilities

Abstract

AbstractIn this article, the robust stochastic stability problem and robust performance problem of discrete‐time Markovian jump linear systems with uncertain transition probabilities are investigated. Based on the Kronecker product and analysis, perturbation bounds are obtained for the robust stochastic stability of the investigated system by transforming the problem into checking whether a class of uncertain matrices is nonsingular. Furthermore, a sufficient and necessary condition for robust stochastic stability is derived. Similarly, by converting the problem to the judgment of the nonsingularity of uncertain matrices, the exact upper and lower bounds for robust performance are obtained. Then, a sufficient and necessary condition for guaranteeing robust performance is obtained. All the results are given in terms of the structured singular value. Finally, numerical examples are presented to show the effectiveness of the proposed results.