An approach to robust stability of matrix polytopes through copositive homogeneous polynomials

Author

Qian, R.X. ; Demarco, C.L.

Author_Institution

Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA

Volume

37

Issue

6

fYear

1992

fDate

6/1/1992 12:00:00 AM

Firstpage

848

Lastpage

852

Abstract

An approach to guaranteeing the stability of a polytope of matrices is proposed. Previous results in the literature have made the obvious connection between various robust stability problems and a test for positivity of a multivariable polynomial. Such results are extended in order to demonstrate that all matrices within a polytope are stable is and only if an associated homogeneous polynomial is strictly copositive. The additional structure obtained by exploiting homogeneity of this multivariable polynomial leads to several computationally tractable sufficiency tests for establishing either robust stability or instability of a polytope of matrices

Keywords

matrix algebra; polynomials; stability criteria; copositive homogeneous polynomials; matrix polytopes; multivariable polynomial; positivity test; robust stability; Computational complexity; Computational efficiency; Costs; Eigenvalues and eigenfunctions; Grid computing; Polynomials; Robust stability; Robustness; Sufficient conditions; System testing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.256360

Filename

256360