Fuzzy switching function-based sliding mode controller design for T-S fuzzy descriptor systems

The design of switching functions is extremely important in the design of sliding mode controllers in that it closely relates to the solvability of the sliding mode control problems. This paper is concerned with the design problems of switching functions and fuzzy sliding mode controllers for T-S fuzzy descriptor systems. First, a generalized regular form of T-S fuzzy descriptor systems is defined. Then the design method of the linear switching function-based fuzzy sliding mode controller is developed and the result obtained indicates a relationship between the design parameter in the switching function and the gain matrix in the controller of T-S fuzzy systems. From this relationship, a new framework of the switching function design for T-S fuzzy descriptor systems is formulated. Moreover, the design method of the fuzzy switching function-based sliding mode controllers is proposed to exemplify the proposed framework. It is shown that the proposed fuzzy switching function-based method is less conservative than the linear switching function-based method from the viewpoint of the solvability of the sliding mode control problems. Finally, the results obtained are verified through four illustrative examples.