Passive estimated state feedback fuzzy controller design for discrete perturbed fuzzy systems with multiplicative noises

This article presents an estimated state feedback fuzzy controller design method for uncertain passive discrete-time nonlinear stochastic systems with multiplicative noises. The nonlinear stochastic systems considered in this article are represented by Takagi-Sugeno (T-S) fuzzy models. For describing stochastic behaviors, stochastic differential equations are used to structure the stochastic T-S fuzzy model for representing nonlinear stochastic systems. Besides, the uncertainties of the controlled system are considered for dealing with molding errors and varying parameters. The concept of parallel distributed compensation is employed in this article to construct the estimated state feedback fuzzy controllers. Applying the Lyapunov and passivity theories, the sufficient stability conditions are derived in terms of linear matrix inequality. Finally, a numerical example is provided to show the effectiveness and applicability of the proposed fuzzy controller design approach.