Stability of discrete-time matrix polynomials

Author

Ngo, Kanh T. ; Erickson, Kelvin T.

Author_Institution

Dept. of Electr. Eng., Missouri Univ., Rolla, MO, USA

Volume

42

Issue

4

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

538

Lastpage

542

Abstract

This paper derives conditions for the stability of discrete-time systems that can be modeled by a vector difference equation, where the variables are m×1 vectors and the coefficients are m×m matrices. Stability of the system is related to the locations of the roots of the determinant of a real m×m matrix polynomial of nth order. In this case, sufficient conditions for the system to be stable are derived. The conditions are imposed on the ∞-norm of two matrices constructed from the coefficient matrices and do not require the computation of the determinant polynomial. The conditions are the extensions of one of the Jury sufficient conditions for a scalar polynomial. An example is used to illustrate the application of the sufficient conditions

Keywords

difference equations; discrete time systems; linear systems; polynomial matrices; stability; vectors; ∞-norm; Jury sufficient conditions; coefficient matrices; discrete-time matrix polynomials; discrete-time systems; m×1 vectors; m×m matrices; scalar polynomial; sufficient conditions; vector difference equation; Control system synthesis; Difference equations; Kalman filters; Kelvin; Polynomials; Predictive control; Predictive models; Stability analysis; Sufficient conditions; Vectors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.566665

Filename

566665