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A converse sum of squares Lyapunov result with a degree bound

Abstract:

Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector field on a bounded set implies the existence of a Lyapunov function which is a sum-of-squares of polynomials. In particular, the main result states that if a system is exponentially stable on a bounded nonempty set, then there exists an SOS Lyapunov function wh...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1109/TAC.2012.2190163

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Institution:
University of Oxford
Division:
MPLS
Department:
Engineering Science
Role:
Author
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Name:
National Science Foundation
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Name:
Engineering and Physical Sciences Research Council
Publisher:
IEEE
Journal:
IEEE Transactions on Automatic Control More from this journal
Volume:
57
Issue:
9
Pages:
2281-2293
Publication date:
2012-01-12
DOI:
EISSN:
1558-2523
ISSN:
0018-9286
Language:
English
Keywords:
Pubs id:
pubs:318839
UUID:
uuid:8dc23ef3-384b-4d38-bbc6-4aedf838c97b
Local pid:
pubs:318839
Source identifiers:
318839
Deposit date:
2013-03-20

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