Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations

Do Wan Kim and Donghwan Lee

Applied Mathematics and Computation, 2025, vol. 487, issue C

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.

Keywords: T-S fuzzy system; Relaxation; Parameterized linear matrix inequality (PLMI); Linear matrix inequality (LMI); Stability (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:487:y:2025:i:c:s009630032400540x

DOI: 10.1016/j.amc.2024.129079

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