A Novel Observer-Based Output Feedback Controller Design for Discrete-Time Fuzzy Systems

This paper addresses the problem of observer-based output feedback controller designs for discrete-time T–S fuzzy systems based on a relaxed approach in which the fuzzy Lyapunov functions are used. Different from the existing two-step method, a single-step linear matrix inequality method is provided for the observer-based controller design. It is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software. The new design method not only overcomes the drawback induced by the two-step approach but also provides less conservative results over some existing results. Finally, the effectiveness of the proposed approach is demonstrated by an example.