Robust stabilization of uncertain non-homogeneous Markov jump linear systems

Abstract

This paper is concerned with the problem of designing a robust state-feedback stabilizer for continuous-time Markov jump linear systems with time varying transition rates, i.e. for a non-homogeneous Markov jump linear system. Transition rates are assumed to be piecewise constant, so the Markov jump linear system is piecewise homogeneous in fact. The system is subject to mode-dependent, time varying but norm-bounded parametric uncertainty. The stabilization method is based on the Lyapunov function approach and uses piecewise constant Lyapunov candidate. The robust stochastic mode-dependent stabilizer is presented in terms of linear matrix inequalities and an illustrative example is provided to verify the theoretical results.