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On the construction of Lyapunov functions using the sum of squares decomposition

Papachristodoulou, Antonis and Prajna, Stephen (2002) On the construction of Lyapunov functions using the sum of squares decomposition. In: Proceedings of the 41st IEEE Conference on Decision and Control. IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 3482-3487. ISBN 0-7803-7516-5.

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A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.

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Additional Information:© 2002 IEEE. Issue Date: 10-13 Dec. 2002. Date of Current Version: 10 March 2003. Work financially supported by AFOSR MURI “Mathematical Infrastructure for Robust Virtual Engineering" and "Unified Theory for Complex Biological and Engineering Networks", NIH/NIGMS AfCS (Alliance for Cellular Signalling), DARPA "Enlightened multiscale simulation of biochemical networks", the Kitano ERATO Systems Biology Project, and URI "Protecting Infrastructures from Themselves."
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI)UNSPECIFIED
NIH/NIGMS Alliance for Cellular Signaling (AfCS)UNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Kitano ERATO Systems Biology ProjectUNSPECIFIED
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INSPEC Accession Number7698511
Series Name:IEEE Conference on Decision and Control
Record Number:CaltechAUTHORS:20111102-095353746
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Official Citation:Papachristodoulou, A.; Prajna, S.; , "On the construction of Lyapunov functions using the sum of squares decomposition," Decision and Control, 2002, Proceedings of the 41st IEEE Conference on , vol.3, no., pp. 3482- 3487 vol.3, 10-13 Dec. 2002 doi: 10.1109/CDC.2002.1184414 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27581
Deposited By: Tony Diaz
Deposited On:04 Nov 2011 15:59
Last Modified:09 Nov 2021 16:49

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