Abstract

Root clustering problems of matrices are considered. Here we are given conditions for eigenvalues of a matrices to lie in a prescribed subregion D of the complex plane. The region D (stability region ) is defined by a rational functions. A simple necessary and sufficient condition for stability of a single matrix is obtained. For the commutting polynomial family a necessary and sufficient condition in term of a common solution to a set of Lyapunov inequalities is derived. A simple sufficient condition for the Hurwitz stability of a commutting quadratic polynomial family is given.

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