H∞ control for fuzzy time-delay systems via descriptor system approach

We consider the H_∞ disturbance attenuation of Takagi-Sugeno fuzzy retarded and neutral type time-delay systems. For these fuzzy time-delay systems, a descriptor system approach is taken to analyze and synthesize fuzzy time-delay systems. We first make an H_∞-norm analysis and obtain sufficient conditions for an H∞-norm to be less than a prescribed number. Sufficient conditions we obtain here depend on the maximum value of time-delay and are given in terms of linear matrix inequalities (LMI). Next, we consider a design problem how to choose control gains. Based on the H_∞-norm analysis, we give time-dependent sufficient conditions for the H_∞-norm of the closed-loop system to be less than a prescribed number. Furthermore, we give a design method in terms of LMI. Finally, a simple example is given to illustrate the theory.