A descriptor representation approach to observer-based control synthesis for discrete-time fuzzy systems

This work is concerned with the observer-based H ∞ control synthesis problem of discrete-time Takagi–Sugeno (T–S) fuzzy systems with external disturbances. The objective is to find a new way to design the controller and observer guaranteeing a prescribed H ∞ performance of the fuzzy system. By the descriptor representation approach, two new conditions for observer-based H ∞ control synthesis are proposed based on various Lyapunov function candidates, which are in the form of linear matrix inequalities (LMIs). A numerical example will be given to show the efficiency of the proposed method.