Algebraic Structure of Generalized Positive Real Matrices

Abstract

Square matrices $Z( \cdot )$ of real rational functions of a complex variable are considered with two properties : (1) $Z(\infty )$ has finite elements; (2) $Z(j\omega ) + Z'( - j\Omega )$ is nonnegative definite Hermitian for all real $\omega $, other than those for which $j\omega $ is a pole of an element of $Z( \cdot )$. Necessary and sufficient conditions for the nonnegativity property are derived which involve the existence of constant. matrices satisfying several algebraic equations. The work thereby extends earlier results on the structure of rational positive real matrices.