Designing mixed fuzzy controller for uncertain stochastic discrete nonlinear systems

By combining with sliding mode control and fuzzy control, this paper proposes a mixed fuzzy controller to guarantee the stabilization of discrete nonlinear systems with parametric uncertainties and bilinear consequent part, which are represented by the Takagi-Sugeno fuzzy systems. Firstly, the sliding surface is defined and the hitting controller is designed to guarantee that the states of the system will converge to the sliding surface. Secondly, a parallel distributed compensation based fuzzy controller can be obtained by solving the corresponding sufficient conditions, which are derived regarding linear matrix inequalities based on the Lyapunov theory. Finally, a numerical example is shown to demonstrate the effectiveness of proposed mixed fuzzy control method.