https://hal.inria.fr/hal-00724864Baier, RobertRobertBaierMathematisches Institut [Bayreuth] - Universität BayreuthGrüne, LarsLarsGrüneMathematisches Institut [Bayreuth] - Universität BayreuthHafstein, Sigurđur FreyrSigurđur FreyrHafsteinReykjavík University - Reykjavík UniversityLinear programming based Lyapunov function computation for differential inclusionsHAL CCSD2012[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Bouzat, Estelle2012-08-22 19:20:102022-01-05 16:04:042012-08-22 19:20:10enJournal articles10.3934/dcdsb.2012.17.331We 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.