H_∞ output feedback control design for discrete-time fuzzy systems

This paper investigates the relaxed non-quadratic stability conditions, fuzzy observer designs and H_∞ controller designs for discrete-time Takagi-Sugeno fuzzy systems based on a relaxed approach in which fuzzy Lyapunov functions are used. First, a new relaxed condition of non-quadratic stability is presented, which is shown to be useful in designing fuzzy controller and observer. Second, new fuzzy observers based on the relaxed non-quadratic stability conditions have been proposed. Then, a sufficient linear matrix inequality (LMI)-type condition is proposed to guarantee the existence of the H_∞ controllers based on the fuzzy observers designed. It is shown that the controller and observer parameters can be obtained by solving a set of LMIs that are numerically feasible with commercially available software. Finally, the effectiveness and less conservativeness of the proposed approach are demonstrated by two examples.