Delay-dependent robust stabilization for uncertain discrete-time fuzzy Markovian jump systems with mode-dependent time delays

This paper deals with the problem of delay-dependent robust stabilization for uncertain discrete-time fuzzy Markovian jump systems with mode-dependent time-varying delays. A delay-dependent stochastic stability condition for a fuzzy Markovian jump system with two levels of structure is obtained based on a new Lyapunov functional. The Lyapunov functional depends not only on the fuzzy basis functions but also on the system modes. Furthermore, a delay-dependent sufficient condition for the solvability of the robust stabilization problem is proposed in terms of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the proposed design method.