Robust stabilization of input constrained uncertain systems with nonhomogeneous Markov switching

Abstract

© 2016 IEEE.This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markov jumps. The uncertainties are assumed to be norm bounded and the transition probabilities are time-varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time-varying transition probabilities inside a polytope, we establish conditions under which the closed-loop system is asymptotically stable. Based on these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality (LMI) constraints. The results are then illustrated by a numerical example.