Published December 2002
| public
Book Section - Chapter
On the construction of Lyapunov functions using the sum of squares decomposition
Chicago
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Abstract
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.
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."Additional details
- Eprint ID
- 27581
- Resolver ID
- CaltechAUTHORS:20111102-095353746
- Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI)
- NIH/NIGMS Alliance for Cellular Signaling (AfCS)
- Defense Advanced Research Projects Agency (DARPA)
- Kitano ERATO Systems Biology Project
- URI
- Created
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2011-11-04Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
- Series Name
- IEEE Conference on Decision and Control
- Other Numbering System Name
- INSPEC Accession Number
- Other Numbering System Identifier
- 7698511