Common Lyapunov function approach to matrix root clustering

摘要

This paper proposes an alternative route to the matrix root clustering problem, which enables to use a result on the common Lyapunov function for solving the problem efficiently. A necessary and sufficient condition is obtained in terms of the existence of a common positive definite solution to a set of Lyapunov inequalities for eigenvalues of a matrix to lie in a prescribed subregion of the complex plane. Applications to root clustering in sector regions are shown for illustration. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 14]