Spectrum localization of regular matrix polynomials and functions. (English) Zbl 1207.15019
Summary: 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.
MSC:
15A42 | Inequalities involving eigenvalues and eigenvectors |
15A22 | Matrix pencils |
15A54 | Matrices over function rings in one or more variables |
26C10 | Real polynomials: location of zeros |
15A45 | Miscellaneous inequalities involving matrices |