Relaxed Conditions for Parameterized Linear Matrix Inequality in the Form of Double Sum

TL;DR

This paper introduces less conservative linear matrix inequalities for parameterized LMIs in double convex sum form, improving stability analysis and control design in T-S fuzzy systems through a novel sum relaxation method.

Contribution

It proposes a new sum relaxation technique based on Young's inequality to derive less conservative LMIs for PLMIs in double convex sum form, enhancing T-S fuzzy system analysis.

Findings

Derived LMIs are less conservative than existing conditions.

The technique improves stability analysis accuracy.

Examples demonstrate the reduced conservatism of the new LMIs.

Abstract

The aim of this study is to investigate less conservative conditions for a parameterized linear matrix inequality (PLMI) expressed in the form of a double convex sum. This type of PLMI frequently appears in T-S fuzzy control system analysis and design problems. In this letter, we derive new, less conservative linear matrix inequalities (LMIs) for the PLMI by employing the proposed sum relaxation method based on Young's inequality. The derived LMIs are proven to be less conservative than the existing conditions related to this topic in the literature. The proposed technique is applicable to various stability analysis and control design problems for T-S fuzzy systems, which are formulated as solving the PLMIs in the form of a double convex sum. Furthermore, examples is provided to illustrate the reduced conservatism of the derived LMIs.