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Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction
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posted on 2023-06-08, 21:10 authored by J Björnsson, Peter GieslPeter Giesl, S Hafstein, C M Kellett, H LiThe numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to compute a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to compute the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose computing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a computation and present several examples to illustrate the utility of this approach.
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Publication status
- Published
Journal
Proceedings of the 53rd IEEE Conference on Decision and Control (CDC)Publisher
IEEEExternal DOI
Page range
5506-5511Book title
2014 IEEE 53rd Annual Conference on Decision and Control (CDC)ISBN
9781479977468Department affiliated with
- Mathematics Publications
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Conference: 15-17 Dec 2014, Los Angeles, CaliforniaFull text available
- No
Peer reviewed?
- Yes
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2015-06-17Usage metrics
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