Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction

Jóhann Björnsson 1 Peter Giesl 2 Sigurdur Hafstein 3 Christopher M. Kellett 4 Huijuan Li 5
1 deCODE Genetics
2 Department of Mathematics [Sussex]
3 Reykjavík University
4 School of Electrical Engineering and Computer Science
5 Department of Computer Science and Engineering
Abstract : The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continu-ous and Piecewise Affine (CPA) method, linear programming is used to parameterize 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 parameterize the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose parameterizing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a parameterization and present several examples to illustrate the utility of this approach.
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Communication dans un congrès
CDC 2014, 2014, Los Angeles, United States. Proceedings of the 53rd IEEE Conference on Decision and Control. 〈http://control.disp.uniroma2.it/CDC2014/〉
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Jóhann Björnsson, Peter Giesl, Sigurdur Hafstein, Christopher M. Kellett, Huijuan Li. Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction. CDC 2014, 2014, Los Angeles, United States. Proceedings of the 53rd IEEE Conference on Decision and Control. 〈http://control.disp.uniroma2.it/CDC2014/〉. 〈hal-01098274〉

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