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

Richard T. O'Brien; Pablo A. Iglesias

doi:10.1109/81.922459

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

Richard T. O'Brien, Pablo A. Iglesias

Whiting School of Engineering

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

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.

Original language	English (US)
Pages (from-to)	565-577
Number of pages	13
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	48
Issue number	5
DOIs	https://doi.org/10.1109/81.922459
State	Published - May 2001

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/81.922459

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

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.",

author = "O'Brien, {Richard T.} and Iglesias, {Pablo A.}",

note = "Funding Information: Manuscript received October 22, 1998; revised June 2000, and December 2000. This work was supported in part by the National Science Foundation under Grants ECS-9309387 and ECS-9800057. This paper was recommended by Associate Editor A. Csurgay. R. T. O{\textquoteright}Brien, Jr., is with the Systems Engineering Department, the United States Naval Academy, Annapolis, MD 21402 USA. P. A. Iglesias is with the Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD 21218 USA. Publisher Item Identifier S 1057-7122(01)03848-X.",

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N2 - 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.

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

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