New Less Conservative Control Design Conditions for T-S Fuzzy Systems: Relaxed Parameterized Linear Matrix Inequality in the Form of Double Sum

The aim of this study is to investigate less conservative conditions for a parameterized linear matrix inequality (PLMI) expressed in the form of double convex sum. This type of PLMI appears frequently in nonlinear T-S fuzzy control analysis and synthesis problems. In this paper, we derive sufficient linear matrix inequalities (LMIs) for the PLMI without using any slack variables, by employing the proposed sum relaxation based on Young's inequality. The derived LMIs are proven to be less conservative than those presented in [1]. The proposed technique is applicable to various control design problems for T-S fuzzy systems represented in PLMIs that take the form of double convex sum. Furthermore, an example is provided to illustrate the reduced conservatism of the derived LMIs