Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises

The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi–Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method.