Valeriu Prepelita: The inertia in the spectral structure of quadratic self-adjoint matrix polynomials, 453-462

Abstract:

A method to determine the inertia for a class of quadratic self-adjoint matrix polynomials is provided, which uses the concepts and the techniques of the spectral theory of self-adjoint matrix polynomials. Two formulas for the signature and the rank of these matrices are derived. Two examples illustrate the proposed methods and their applications to feedback stabilization of a class of control systems.

Key Words: inertia, self-adjoint matrix polynomial, quadratic matrix, eigenvalues, sign characteristic, feedback stabilization.

2010 Mathematics Subject Classification: Primary 15A57, Secondary 15A18, 15A54, 93D15.