A Characterization of Diagonal Solutions for a Class of Linear Matrix Inequality
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6417Keywords:
diagonal matrices, $P$-matrix, positive definite matrix, matrix inequality, matrix stabilityAbstract
This paper investigates the existence of positive diagonal solutions for a class of linear matrix inequalities (LMIs) involving a triple of real $n \times n$ matrices $(A_1, A_2, A_3)$. We provide equivalent conditions linking the negative definiteness of a structured block matrix to properties of positive semidefinite test matrices and $P$-matrices under Hadamard transformations. Our results extend classical stability theory, offering new characterizations with applications in control theory~\cite{Boyd1994,Gahinet1994} and network dynamics.
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Copyright (c) 2025 Ali Algefary, Tulin Alhumaidan
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