Abstract:

The L2-L∞ fuzzy control problem of a class of nonlinear Markov jump systems (MJSs) with uncertain transition jump rates is studied. The uncertain transition jump rates are assumed unknown but bounded. By means of Takagi Sugeno fuzzy models, the overall closed loop fuzzy dynamic equalities are constructed through selected membership functions. Based on the L2-L∞ fuzzy control theory, the sufficient condition for the existence of modedependent fuzzy controller is given so that the fuzzy MJSs are stochastically stable for all admissible uncertainties and satisfy the given L2-L∞ control index. By using the constructed LyapunovKrasovskii function and applying linear matrix inequality techniques, the design scheme of the robust L2-L∞ fuzzy controller is derived and described as an optimization one. Simulation results demonstrate the validity of the proposed approach.