Stochastic stability analysis of Markovian jump linear systems with incomplete transition descriptions

Abstract

In this study, the authors focus on the stability analysis for Markovian jump linear systems with partly known transition rates in the continuous-time domain and partly known transition probabilities in the discrete-time domain. By using the properties of the transition rates and transition probabilities, two new sufficient conditions are derived for the stochastic stability of the continuous-time and discrete-time Markovian jump linear systems, respectively. The main advantage of the proposed stability conditions is that the total number of linear matrix inequalities (LMIs) in the proposed stability conditions is much less than that in some existing results. Based on the presented stability conditions, two state feedback controllers are designed for the considered systems in terms of LMIs. In addition, two kinds of stability criteria are developed for the stochastic stability of the considered systems with incomplete transition descriptions by the existence of the unique positive definite solution of the coupled Lyapunov matrix equations. Finally, two numerical examples and one practical example are provided to verify the correctness of the theoretical results.