- Title
- Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction
- Creator
- Hafstein, Sigurður; Kellett, Christopher M.; Li, Huijuan
- Relation
- 2014 American Control Conference ACC. Proceedings of 2014 American Control Conference ACC (Portland, Oregon 04-06 June, 2014) p. 548-553
- Publisher Link
- http://dx.doi.org/10.1109/ACC.2014.6858660
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- conference paper
- Date
- 2014
- Description
- We present a novel numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. Our proposed approach constructs a continuous piecewise affine (CPA) function given a suitable partition of the state space, called a triangulation, and values at the vertices of the triangulation. The vertex values are obtained from a Lyapunov function in a classical converse Lyapunov theorem and verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Furthermore, by refining the triangulation, we show that it is always possible to construct a CPA Lyapunov function. Numerical examples are presented demonstrating the effectiveness of the proposed method.
- Subject
- computational methods; nonlinear systems; Lyapunov methods; asymptotic stability
- Identifier
- http://hdl.handle.net/1959.13/1064163
- Identifier
- uon:17486
- Identifier
- ISBN:9781479932740
- Language
- eng
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