Observer-based fuzzy control design with adaptation to delay parameter for time-delay systems

This paper is concerned with the problem of observer-based fuzzy stabilization for time-delay systems. The time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A new design method is proposed for an observer-based fuzzy controller with adaptation to the time-delay. The designed controller simultaneously contains both the current and past state information of the systems and can be derived by solving a set of linear matrix inequalities (LMIs). The existence of the controller is equivalent to that of a controller for time-delay systems where the constant time-delay is known exactly. A numerical example is given to illustrate the effectiveness of the design method.