Relaxation analysis via line integral

In this paper, sufficient LMI conditions for the H_∞ state feedback control synthesis of fuzzy control systems consisting of Takagi-Sugeno fuzzy models are proposed for continuous fuzzy systems. Based on a premise-dependent Lyapunov function, we release the conservatism that commonly exists in the common P approach. Particularly, the restriction embedded in continuous-time systems on derivative of μ is removed by introducing Lie derivative to the Lyapunov approach. It is shown that the slack variables employed in this paper provide additional feasibility in solving the H _∞ stabilization problem of fuzzy control systems. Consequently, the stabilization conditions are shown to be more relaxed than others in the existing literature. Numerical simulations appear promising for the proposed method and illuminate the reduction of conservatism clearly.