Robust sliding mode fuzzy control for perturbed nonlinear stochastic systems subject to input and state requirements

A robust sliding mode fuzzy control problem of uncertain stochastic nonlinear systems is discussed subject to multiple performance requirements in this paper. The considered requirements focus on robust stability, strict input passivity and individual state constraint at the same time. In order to achieve robust performance, a reaching controller is designed to achieve the proposed integral sliding surface. Besides, a concept of Parallel Distributed Compensation (PDC) is used to design a fuzzy controller to guarantee individual variance constraint and strict input passivity. Based on Lyapunov theory, some sufficient conditions are derived into linear matrix inequality form that can be directly solved by the convex optimization algorithm. Based on the proposed design method, a robust sliding mode fuzzy controller can be established to guarantee multiple performance constraints for uncertain stochastic nonlinear systems. Finally, a numerical example for the control of ship steering systems is employed to demonstrate the effectiveness and application of the proposed design method.