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

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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https://hal.inria.fr/hal-01098274
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, December 23, 2014 - 3:34:26 PM
Last modification on : Thursday, March 12, 2020 - 1:38:01 PM
Long-term archiving on: : Tuesday, March 24, 2015 - 10:41:18 AM

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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. ⟨hal-01098274⟩

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