Relaxed Conditions for Parameterized Linear Matrix Inequality in the Form of Nested Fuzzy Summations

TL;DR

This paper introduces less conservative conditions for parameterized linear matrix inequalities in fuzzy systems using AM-GM inequality, improving stability analysis and control design accuracy.

Contribution

It develops new less conservative PLMI conditions for T-S fuzzy systems by applying AM-GM inequality to handle intersecting membership functions.

Findings

Proposed conditions are less conservative than existing methods.

Method effectively manages product of membership functions with intersecting indices.

Empirical case studies validate improved performance.

Abstract

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.