Cancellations in multivariable continuous-time and discrete-time feedback systems treated by greatest common divisor extraction

Author

Desoer, Charles A. ; Schulman, J.D.

Author_Institution

University of California, Berkeley, CA, USA

Volume

Issue

fYear

1973

fDate

8/1/1973 12:00:00 AM

Firstpage

401

Lastpage

402

Abstract

This correspondence considers a multivariable system with proper rational matrix transfer functions G0and Gfin the forward and feedback branches, respectively. It develops a strictly algebraic procedure to obtain polynomials whose zeros are the poles of the matrix transfer functions from input to output (Hy), and from input to error (He). G0and Gfare given in the polynomial matrix factored form $N_{0}D_{0}^{-1}$ and $D_{f}^{-1}N_{f}$ . The role of the assumption det [ $I + G_{f}(\\infty )G_{0}(\\infty )] \\neq 0$ and the relation between the zeros of det [ $I + G_{f}G_{0}$ ] and the poles of Hyand Heare indicated. The implications for stability analysis of continuous-time as well as discrete-time systems are stressed.

Keywords

Polynomial matrices; Stability; Transfer function matrices; Circuit theory; Feedback; Helium; Linear systems; MIMO; Notice of Violation; Poles and zeros; Polynomials; Stability analysis; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1973.1100335

Filename

1100335

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=812345