Sliding mode fuzzy control for Takagi–Sugeno fuzzy systems with bilinear consequent part subject to multiple constraints.

This paper investigated the multiple performance constrained sliding mode fuzzy control problem for continuous-time stochastic nonlinear systems with multiplicative noises. The stochastic nonlinear systems considered in this paper are represented by Takagi–Sugeno (T–S) fuzzy models with a bilinear consequent part. To simultaneously satisfy stability, passivity and variance constraints, sufficient conditions are derived in terms of linear matrix inequalities based on Lyapunov theory. By solving the corresponding sufficient conditions, a parallel distributed compensation based fuzzy controller is obtained to ensure the stability of the closed-loop nonlinear systems subject to variance and passivity performance constraints. The main contribution of this paper is a sliding mode fuzzy controller developed such that the considered multiple performance constraints can be satisfied for the T–S fuzzy systems with a bilinear consequent part. Finally, a numerical example for controlling a ship steering system is provided to demonstrate the validity and effectiveness of the proposed sliding mode fuzzy control method. [ABSTRACT FROM AUTHOR]