Stability and Stabilization for Discrete-time Markovian Jump Fuzzy Systems with Time-varying Delays: Partially Known Transition Probabilities Case

This paper focuses on the stability analysis and the stabilization problem for a discrete-time Markovian jump fuzzy systems (MJFSs) with time-varying delays and partially known transition probabilities. These systems are made more general, by relaxing the traditional assumption in MJFSs that all the transition probabilities must be completely known. The class of MJFSs considered is described by a fuzzy model composed of two levels: a crisp level that represents the jumps and a fuzzy level that represents the system nonlinearities. Based on a stochastic Lyapunov function, stability and stabilization conditions for the MJFSs with time-varying delays are derived in both the case of completely known transition probabilities and the case of partially known transition probabilities. The derived conditions are represented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the effectiveness of the proposed theorem.