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Revised CPA method to compute Lyapunov functions for nonlinear systems
journal contribution
posted on 2023-06-08, 21:10 authored by Peter GieslPeter Giesl, Sigurdur F HafsteinThe 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.
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Publication status
- Published
File Version
- Accepted version
Journal
Journal of Mathematical Analysis and ApplicationsISSN
0022-247XPublisher
ElsevierExternal DOI
Issue
1Volume
410Page range
292-306Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2015-06-16First Open Access (FOA) Date
2017-01-17First Compliant Deposit (FCD) Date
2017-01-17Usage metrics
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