An extension of the Levy-Desplanque theorem and some stability conditions for matrices with uncertain entries

Author

Naimark, Leonid ; Zeheb, Ezra

Author_Institution

Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa, Israel

Volume

44

Issue

2

fYear

1997

fDate

2/1/1997 12:00:00 AM

Firstpage

167

Lastpage

170

Abstract

Sufficient conditions for Hurwitz stability and for the “degree of stability” of a family of complex matrices with uncertain entries in bounded sets in the complex plane, are derived. The Levy-Desplanque theorem is extended in two directions: the requirement for strict diagonal dominance is alleviated and the (alleviated) theorem is made applicable to families of matrices with uncertain entries. Also, sufficient conditions for Schur stability and for Schur “degree of stability” of a family of real interval matrices are derived. All the above sufficient conditions, as well as the Levy-Desplanque theorem extension, are remarkable in their simplicity to carry out and in the rich variety of possibilities of using them

Keywords

eigenvalues and eigenfunctions; matrix algebra; numerical stability; Hurwitz stability; Levy-Desplanque theorem extension; Schur stability; complex matrices; real interval matrices; stability conditions; uncertain entries; Circuits; Computational complexity; Eigenvalues and eigenfunctions; Equations; Polynomials; Robust stability; Sufficient conditions; Symmetric matrices; Systems engineering and theory; Uncertainty;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.554337

Filename

554337