Further studies on H∞ observer design for continuous-time Takagi–Sugeno fuzzy model

Abstract This brief paper is concerned with the problem of observer-based H ∞ control for nonlinear systems presented by T–S (Takagi–Sugeno) fuzzy models. The aim is to reduce the conservatism of finding a smaller H ∞ performance index by applying the non-quadratic Lyapunov function. The one-step LMIs (Linear Matrix Inequalities) method is applied to design the controller gains and observer gains. In addition, the initial positions of the observer states are also discussed and an optimization problem is solved to obtain new stable region. In the end, three examples are given to demonstrate the effectiveness of the proposed approach.