Conditions for the 2-D characteristic polynomial of a matrix to be very strict Hurwitz

Author

Agathoklis, P.

Author_Institution

Dept. of Electr. & Comput. Eng., Victoria Univ., BC, Canada

fYear

1988

fDate

11-14 Apr 1988

Firstpage

856

Abstract

Conditions for the bi-variate characteristic polynomial of a matrix to be very strict Hurwitz are presented. These conditions are based on two different formulations of the 2-D continuous Lyapunov equation. The necessary and sufficient conditions for the existence of positive definite solutions for the first formulation with constant coefficients are presented. It is shown that such an existence is only sufficient but not necessary for the characteristic polynomial to be very strict Hurwitz. Further, the testing of zeros at infinite distant points requires the use of a class of very strict positive real functions. An alternative formulation of the Lyapunov equation with frequency dependent coefficients is also presented based on a new condition for the very strict Hurwitz property. This second formulation of the Lyapunov equation leads to necessary and sufficient conditions for the very strict Hurwitz property

Keywords

Lyapunov methods; matrix algebra; polynomials; stability; 2-D continuous Lyapunov equation; bi-variate characteristic polynomial; constant coefficients; frequency dependent coefficients; infinite distant points; matrix; positive definite solutions; positive real functions; testing; very strict Hurwitz; zeros; Continuous time systems; Differential equations; Frequency dependence; Frequency domain analysis; Polynomials; Stability analysis; Sufficient conditions; System testing;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on

Conference_Location

New York, NY

ISSN

1520-6149

Type

conf

DOI

10.1109/ICASSP.1988.196721

Filename

196721