  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.
