${\cal H}_\infty$ State-Feedback-Control Design for Discrete-Time Fuzzy Systems Using Relaxation Technique for Parameterized LMI

In this study, we establish a less-conservative
H
_ stabilization condition for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To this end, we propose a useful relaxation technique that can be used to transform parameterized-linear-matrix inequalities (PLMIs) with homogeneous polynomial dependence on current-time parameters and preceding parameters into a finite set of LMIs. The main feature of this technique is that all possible slack variables can be included in the relaxation process to fully exploit the convexity of the PLMIs. By applying the relaxation technique, we establish a less-conservative LMI-based
H
_ stabilization condition.