Revised CPA method to compute Lyapunov functions for nonlinear systems
By Peter Giesl, Sigurdur Freyr Hafstein. 2014
80 citations recorded by the source corpus.
The CPA method uses linear programming to compute Continuous and Piecewise Affine Lyapunov function for nonlinear systems with asymptotically stable equilibria. In it was shown that the method always succeeds in computing a CPA Lyapunov function for such a system. The size of the domain of the computed CPA Lyapunov function is only limited by the equilibrium’s basin of attraction. However, for some systems, an arbitrary small neighborhood of the equilibrium had to be excluded from the domain a priori. This is necessary, if the equilibrium is not exponentially stable, because the existence of a CPA Lyapunov function in a neighborhood of the equilibrium is equivalent to its exponential stability as shown in. However, if the equilibrium is exponentially stable, then this was an artifact of the method. In this paper we overcome this artifact by developing a revised CPA method. We show that this revised method is always able to compute a CPA Lyapunov function for a system with an exponentially stable equilibrium. The only conditions on the system are that it is C² and autonomous. The domain of the CPA Lyapunov function can be any a priori given compact neighborhood of the equilibrium which is contained in its basin of attraction. Whereas in a previous paper we have shown these results for planar systems, in this paper we cover general n-dimensional systems.
Subfields: Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/ae50cc2eb7448f0ec393f38887b69d89a01d6b31
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In Control and Systems Engineering
In Numerical Analysis
Citations in the corpus
- Review on computational methods for Lyapunov functions (2015, methodology): “…in Hafstein 2007 [110] to arbitrarily switched, non-autonomous systems, in Baier, Gr¨une, and Haf-stein 2010 [19] to differential inclusions, in Giesl and Hafstein 2014 [93] to discrete-time systems, and in Li, Baier, Hafstein, Gr¨une, and Wirth 2014, 2015 [148, 149] to ISS Lyapunov…”