Spectrum localization of regular matrix polynomials and functions

Abstract

This paper is devoted to the spectrum localization problem for regular matrix polynomials and functions. Sufficient conditions are proposed for spectrum placement in a wide class of regions bounded by analytical curves. These conditions generalize the known linear matrix inequalities (LMI) approaches to stability analysis and pole placement of polynomial matrices. In addition, a method of robust spectrum placement is developed in the form of the LMI systems for a parametric set of matrix polynomials.