Stochastic Stability Analysis and Stabilization

This chapter focuses on the stochastic stability analysis and the stabilizing controller design problem for discrete-time Markov jump singularly perturbed systems (MJSPSs), in which the complete probability information case, partial probability information case and general probability information case are fully considered. First, by utilizing the properties of the transition probabilities and the Lyapunov function approach, a set of solvable sufficient conditions for the stochastic stability of MJSPSs are proposed in terms of linear matrix inequalities for the complete probability information case, partial probability information case and general probability information case. Based on the presented conditions, the mode-dependent stabilizing controller gains and mode-independent stabilizing controller gains can be obtained for the complete probability information case, partial probability information case and general probability information case. Finally, a numerical example is provided to verify the effective of the theoretical results.