an:06015373
Zbl 1235.93222
Baier, Robert; Gr??ne, Lars; Hafstein, Sigur??ur Freyr
Linear programming based Lyapunov function computation for differential inclusions
EN
Discrete Contin. Dyn. Syst., Ser. B 17, No. 1, 33-56 (2012).
00296411
2012
j
93D30 93D20 34D20 34A60 34A36
Lyapunov functions; stability of nonlinear systems; numerical construction of Lyapunov functions; invariance principle; differential inclusions; switched systems; piecewise affine functions
Summary: 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.
Reviewer (Berlin)