On the poles and zeros of linear, time-varying systems

Author

Brien, Richard T O, Jr. ; Iglesias, Pablo A.

Author_Institution

Syst. Eng. Dept., United States Naval Acad., Annapolis, MD, USA

Volume

48

Issue

5

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

565

Lastpage

577

Abstract

Definition of poles and zeros are presented for continuous-time, linear, time-varying systems. For a linear, time-varying state equation, a set of time-varying poles defines a stability-preserving variable change relating the original state equation to an upper triangular state equation. A zero is a function of time corresponding to an exponential input whose transmission to the output is blocked. Both definitions are shown to be generalizations of existing definitions of poles and zeros for linear, time-varying systems and are consistent with the definitions for linear, time-invariant systems. A computation procedure is presented using a QR decomposition of the transition matrix for the state equation. A numerical example is given to illustrate this procedure

Keywords

continuous time systems; linear systems; matrix decomposition; poles and zeros; stability; time-varying systems; QR decomposition; blocked transmission; computation procedure; continuous-time linear systems; exponential input; linear time-varying state equation; linear time-varying systems; poles and zeros; stability-preserving variable change; time-varying poles; transition matrix; upper triangular state equation; Differential equations; H infinity control; Helium; Matrix decomposition; Poles and zeros; Robustness; Stability; Systems engineering and theory; Time varying systems; 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

10.1109/81.922459

Filename

922459