Constrained overall controller of fuzzy stochastic jump systems

This paper deals with the problem of constrained fuzzy controller design for a class of continuous-time nonlinear systems with Markovian jumps. By means of Takagi-Sugeno fuzzy models, the overall nonlinear controller is constructed by blending local linear controllers through selected membership functions. The local controllers have the mode-dependent gains governed by stochastic transition rate matrix. The constraint condition of control input is studied here to guarantee certain amplitude level, where the notation of maximum norm covering the overall system is used. The sufficient condition for the existence of mode-dependent state feedback controller with control constraints is derived, which can guarantee the stochastic stability of the closed-loop fuzzy jump systems. The design methods in which the norm constraints are imposed on the control input are formulated as linear matrix inequalities problems. Finally, a numerical example is given to illustrate the design procedure