Fuzzy Descriptor Sliding Mode Observer Design: A Canonical Form-Based Method

Linear switching function and integral-type switching function are two typical switching functions in the sliding mode control field. Based on these, this paper investigates the design problem of fuzzy descriptor sliding mode observers. Two canonical forms, which are the T-S fuzzy descriptor systems' counterparts of the canonical form in normal systems, are first proposed. In terms of the proposed canonical forms, a linear switching function-based fuzzy descriptor sliding mode observer and an integral-type switching function-based fuzzy descriptor sliding mode observer are designed, respectively. It is shown that although the linear switching function-based fuzzy descriptor sliding mode observer has a much simpler design structure than the integral-type switching function-based fuzzy descriptor sliding mode observer, the integral-type switching function-based design method can deal with a much larger range of T-S fuzzy descriptor systems than the linear switching function-based design method. Finally, three simulation examples are provided to verify the effectiveness and merits of the proposed method.