Stochastic stabilization of uncertain Markov jump linear systems with time varying transition rates

This work deals with the robust stochastic stabilization problem for continuous-time Markov jump linear systems with time varying transition rates, i.e. for a non-homogeneous Markov jump linear system. Norm bounded time varying uncertainties are affecting the system states. Transition rates are assumed to be piecewise constant and in fact the Markov jump linear system is piecewise homogeneous. Based on the multiple Lyapunov function a sufficient condition is derived for robust stochastic stabilization of the system. The conditions are formulated by linear matrix inequalities and thus can be checked easily. One illustrative numerical example is provided to demonstrate the effectiveness of the developed approach.