Robust stability analysis of time-varying systems using time-varying quadratic forms

Jeff S. Shamma

doi:10.1016/0167-6911(94)00010-S

Robust stability analysis of time-varying systems using time-varying quadratic forms

Jeff S. Shamma^*

^*Corresponding author for this work

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

5 Scopus citations

Abstract

We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.

Original language	English (US)
Pages (from-to)	13-17
Number of pages	5
Journal	Systems and Control Letters
Volume	24
Issue number	1
DOIs	https://doi.org/10.1016/0167-6911(94)00010-S
State	Published - Jan 9 1995
Externally published	Yes

Keywords

Quadratic forms
Robust stability
Structured uncertainty
Time-varying systems

ASJC Scopus subject areas

Mechanical Engineering
General Computer Science
Electrical and Electronic Engineering
Control and Systems Engineering

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10.1016/0167-6911(94)00010-S

Cite this

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abstract = "We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.",

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note = "Funding Information: * Supported by grants from Eglin Air Force Base, NSF grants #ECS-9296074 and #ECS-9258005, and a University Research Institute Summer Research Award.",

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Y1 - 1995/1/9

N2 - We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.

AB - We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.

KW - Quadratic forms

KW - Robust stability

KW - Structured uncertainty

KW - Time-varying systems

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Robust stability analysis of time-varying systems using time-varying quadratic forms

Abstract

Keywords

ASJC Scopus subject areas

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