Reducing Conservatism in an $H_{\infty }$ Robust State-Feedback Control Design of T–S Fuzzy Systems: A Nonmonotonic Approach

This paper proposes an H
_∞
robust state-feedback controller design for uncertain Takagi-Sugeno fuzzy systems using a nonmonotonic Lyapunov function. In the nonmonotonic approach, the monotonicity requirement of the Lyapunov function is relaxed by allowing it to increase locally. Based on the nonmonotonic Lyapunov function approach, sufficient conditions for the existence of a robust state-feedback H
_∞
controller that guarantees stability and a prescribed H
_∞
performance are given in terms of linear matrix inequalities. The proposed design technique is shown to be less conservative than the existing k-samples variations of the Lyapunov function. The effectiveness of the proposed approach is further illustrated via numerical examples.