A modified positive-real type stability condition

Alexander Lanzon*, Ian R. Petersen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

39 Citations (Scopus)

Abstract

Lightly damped structures with colocated (position) sensors and (force) actuators can typically be modeled by a (possibly infinite) sum of second order transfer functions. Since the relative degree of these systems is more than unity, they are not directly amenable to standard positive real analysis and since these systems are highly resonant, application of the small gain theorem would be usually very conservative. However, a condition for the internal stability of a positive feedback interconnection of two such systems has been available in the theory of positive position control. This result has important implications on stability robustness due to spill-over dynamics. In this paper, we propose a new stability analysis result which generalizes the positive position control stability result to the feedback interconnection of systems satisfying a certain modified positive-real type condition. Broadly speaking, the result states that a necessary and sufficient condition for the internal stability of the feedback interconnection of such systems is that the DC loop gain is less than unity.

Original languageEnglish
Title of host publication2007 European Control Conference, ECC 2007
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3912-3918
Number of pages7
ISBN (Electronic)9783952417386
DOIs
Publication statusPublished - 2007
Externally publishedYes
Event2007 9th European Control Conference, ECC 2007 - Kos, Greece
Duration: 2 Jul 20075 Jul 2007

Publication series

Name2007 European Control Conference, ECC 2007

Conference

Conference2007 9th European Control Conference, ECC 2007
Country/TerritoryGreece
CityKos
Period2/07/075/07/07

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