Linear algebraic properties of the realization matrix with applications to principal axis realizations

Author

Maskarinec, Gregory J. ; Chitrapu, Prabhakar Rao

Author_Institution

Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA, USA

Volume

39

Issue

8

fYear

1992

fDate

8/1/1992 12:00:00 AM

Firstpage

628

Lastpage

640

Abstract

Examines the realization matrix R=[A b; c d] defined by a state variable model of a linear, shift invariant, discrete time, scalar system. Several properties concerning the eigenvalues and singular values are derived, which are used to obtain tests for the minimality of the state variable model. An inequality is derived between the spectral norm of R and the L_Ω-norm of its frequency response. The realization matrices of principal axis realizations are characterized in terms of their eigenvalues and singular values. qr-factorizations and bounds for the spectral norms of such realization matrices are derived

Keywords

discrete time systems; eigenvalues and eigenfunctions; frequency response; linear systems; matrix algebra; state-space methods; eigenvalues; frequency response; linear shift-invariant discrete-time system; minimality; principal axis realizations; qr-factorizations; realization matrix; singular values; spectral norm; state variable model; Digital filters; Eigenvalues and eigenfunctions; Frequency response; Helium; Linear matrix inequalities; Logic; Numerical analysis; Polynomials; Testing; Transfer functions;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.168929

Filename

168929