New approaches on H∞ control of T–S fuzzy systems with interval time-varying delay

This paper considers the delay-dependent stabilization problems and H∞ control problems for uncertain T–S fuzzy system with time-varying delay in a range. A new method is proposed by defining new Lyapunov functionals and introducing some integral inequalities. The merit of the proposed conditions lies in the less conservativeness than the existing ones, which is achieved by paying careful attention to the subtle difference between the two integral terms, which is always ignored in the existing literatures, and the free variables which replace the Leibniz–Newton formula with integral inequalities. The fuzzy state feedback gains are derived through the numerical solution of a set of linear matrix inequalities (LMIs). The efficiency and the benefits of our method are demonstrated by the numerical examples.