Robust fuzzy control for uncertain stochastic time-delay Takagi–Sugeno fuzzy models for achieving passivity

This paper focuses on the robust passive stability and stabilization problems for uncertain nonlinear stochastic time-delay systems. Via the fuzzy modeling approach, the nonlinear stochastic system is described by Takagi–Sugeno (T–S) fuzzy model in which the consequent parts are presented by linear stochastic time-delay differential equation. With Lyapunov–Krasovskii function and improved Jensen's inequality, the stability criteria are derived. In addition, the passivity theory is employed to discuss external disturbance effect on system for achieving attenuation performance. According to the proposed design method, the fuzzy controller is carried out by parallel distributed compensation (PDC) concept to guarantee the robust asymptotical stability and attenuation performance of system in the sense of mean square. Finally, a synchronous generator power system is presented to manifest the application and effectiveness of the proposed fuzzy control method.