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Construction of Lyapunov functions for nonlinear planar systems by linear programming

journal contribution
posted on 2023-06-08, 05:52 authored by Peter GieslPeter Giesl, Sigurdur Hafstein
Recently the authors proved the existence of piecewise affine Lyapunov functions for dynamical systems with an exponentially stable equilibrium in two dimensions (Giesl and Hafstein, 2010 [7]). Here, we extend these results by designing an algorithm to explicitly construct such a Lyapunov function. We do this by modifying and extending an algorithm to construct Lyapunov functions first presented in Marinosson (2002) [17] and further improved in Hafstein (2007) [10]. The algorithm constructs a linear programming problem for the system at hand, and any feasible solution to this problem parameterizes a Lyapunov function for the system. We prove that the algorithm always succeeds in constructing a Lyapunov function if the system possesses an exponentially stable equilibrium. The size of the region of the Lyapunov function is only limited by the region of attraction of the equilibrium and it includes the equilibrium.

History

Publication status

  • Published

Journal

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

Publisher

Elsevier

Issue

1

Volume

388

Page range

463-479

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-07-23

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