This letter studies less conservative conditions for a parameterized linear matrix inequality (PLMI) in the form of double convex sum. Without any slack variables, sufficient linear matrix inequalities (LMIs) for the PLMI are derived by using the proposed sum relaxation based on Young's inequality. It is proved that the derived LMIs are not conservative than those of Tuan et al in 2001. An example is given to show the reduced conservatism of the derived LMIs.

中文翻译：

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以双和形式放宽 PLMI

这封信研究了双凸和形式的参数化线性矩阵不等式 (PLMI) 不太保守的条件。在没有任何松弛变量的情况下，PLMI 的足够线性矩阵不等式 (LMI) 是通过使用基于杨氏不等式提出的总和松弛得出的。证明了推导的 LMI 并不比 Tuan 等人在 2001 年的保守。给出一个例子来说明推导的 LMI 的保守性降低。