Linear programming based Lyapunov function computation for differential inclusions
By Robert Baier, Lars Grüne, Sigurdur Freyr Hafstein. 2011
67 citations recorded by the source corpus.
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.
Subfields: Control and Systems Engineering, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fa34d62de5e8c5d8e5b14a282cce020153e2f3be
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In Control and Systems Engineering
In Geometry and Topology
Citations in the corpus
- Review on computational methods for Lyapunov functions (2015, methodology): “The CPA method has been extended to more general systems: in Hafstein 2007 [110] to arbitrarily switched, non-autonomous systems, in Baier, Grüne, and Hafstein 2012 [19] to differential inclusions, in Giesl and Hafstein 2014 [93] to discretetime systems, and in Li, Baier, Hafstein, Grüne, and Wirth ”
- Computation of local ISS Lyapunov functions for discrete-time systems via linear programming (2016, background): “i i i i Furthermore, this result was extended to asymptotically stable systems [8], to asymptotically stable, arbitrarily switched, non-autonomous systems [9], and to asymptotically stable differential inclusions [1].”