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.