H∞-control for Takagi-Sugeno fuzzy descriptor systems

The design problem of output feedback H_∞ controllers for Takagi-Sugeno fuzzy descriptor models is considered. We first give the sufficient conditions for the admissibility of the Takagi-Sugeno fuzzy descriptor systems. Then we introduce the H_∞-performance (norm) for a stable fuzzy descriptor system and give a sufficient condition for the norm being less than a given number. We also consider the H_∞-problem with output feedback controllers. As for the premise variable in the if-then rules, we consider three cases where the premise variable is a given function, the output, and the descriptor variable of the underlying system