Lyapunov functions for uncertain systems with applications to the stability of time varying systems

SOURA DASGUPTA; GANAPATHY CHOCKALINGAM; B. D. O ANDERSON; MINYUE FU

doi:10.1109/81.269046

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Journal article

Lyapunov functions for uncertain systems with applications to the stability of time varying systems

SOURA DASGUPTA, GANAPATHY CHOCKALINGAM, B. D. O ANDERSON and MINYUE FU

IEEE transactions on circuits and systems. 1, Fundamental theory and applications, Vol.41(2), pp.93-106

1994

DOI: 10.1109/81.269046

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Abstract

This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant if there exist multiaffinely parameterized positive definite, Lyapunov matrices that solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are strictly positive real if the Lyapunov matrices solving the equations featuring in the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of linear time varying systems.

Applied Sciences

System Theory

Control theory. Systems

Exact sciences and technology

Computer science; control theory; systems

Details

Title: Subtitle: Lyapunov functions for uncertain systems with applications to the stability of time varying systems
Creators: SOURA DASGUPTA - Univ. Iowa, dep. electrical computer eng., Iowa City IA 52242, United States
GANAPATHY CHOCKALINGAM - Univ. Iowa, dep. electrical computer eng., Iowa City IA 52242, United States
B. D. O ANDERSON - Univ. Iowa, dep. electrical computer eng., Iowa City IA 52242, United States
MINYUE FU - Univ. Iowa, dep. electrical computer eng., Iowa City IA 52242, United States
Resource Type: Journal article
Publication Details: IEEE transactions on circuits and systems. 1, Fundamental theory and applications, Vol.41(2), pp.93-106
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/81.269046
ISSN: 1057-7122
eISSN: 1558-1268
Language: English
Date published: 1994
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984083238102771

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