H∞ constrained fuzzy control via state observer feedback for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises

The purpose of this paper is to study the H∞ constrained fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises by using the state observer feedback technique. The proposed fuzzy controller design approach is developed based on the Parallel Distributed Compensation (PDC) technique. Through the Lyapunov stability criterion, the stability analysis is completed to develop stability conditions for the closed-loop systems. Besides, the H∞ performance constraints is also considered in the stability condition derivations for the worst case effect of disturbance on system states. Solving these stability conditions via the two-step Linear Matrix Inequality (LMI) algorithm, the observer-based fuzzy controller is obtained to achieve the stability and H∞ performance constraints, simultaneously. Finally, a numerical example is provided to verify the applicability and effectiveness of the proposed fuzzy control approach.