  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.
