Linear programming based Lyapunov function computation for differential inclusions

Robert Baier 1 Lars Grüne 1 Sigurđur Freyr Hafstein 2
1 Mathematisches Institut [Bayreuth]
2 Reykjavík University
Abstract : We present a numerical algorithm for computing Lyapunov functions for a class of strongly asymptotically stable nonlinear differential inclusions which includes spatially switched systems and systems with uncertain parameters. The method relies on techniques from nonsmooth analysis and linear programming and constructs a piecewise affine Lyapunov function. We provide necessary background material from nonsmooth analysis and a thorough analysis of the method which in particular shows that whenever a Lyapunov function exists then the algorithm is in principle able to compute it. Two numerical examples illustrate our method.
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Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2012, 17 (1), pp.33-56. 〈10.3934/dcdsb.2012.17.33〉
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Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 19:20:10
Dernière modification le : vendredi 13 octobre 2017 - 17:08:16

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Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2012, 17 (1), pp.33-56. 〈10.3934/dcdsb.2012.17.33〉. 〈hal-00724864〉

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