Stabilization on fuzzy Markovian jump systems with uncertain switching probabilities

This paper is concerned with the robust control problem for fuzzy Markovian time-delay jump systems with uncertain switching probabilities. The transition rate matrix of the Markov process and the parameters of the system are uncertain but belong to a given polytope. By applying Lyapunov stability theory and free-weighting matrix method, a new delay-dependent stabilization criterion for the fuzzy Markovian jump systems is derived in terms of linear matrix inequalities (LMIs). The fuzzy state feedback controller gain is characterized in terms of the solution to the delay-dependent linear matrix Inequalities. Designed controller can guarantee asymptotically stable in mean square of the resulting closed-loop system for all admissible uncertainties and time delay.