Skip to Main content Skip to Navigation
Documents associated with scientific events

Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction

Abstract : 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.
Document type :
Documents associated with scientific events
Complete list of metadata

Cited literature [2 references]  Display  Hide  Download

https://hal.inria.fr/hal-01025882
Contributor : Hasnaa Zidani <>
Submitted on : Friday, July 18, 2014 - 3:49:38 PM
Last modification on : Friday, August 23, 2019 - 3:08:02 PM
Long-term archiving on: : Monday, November 24, 2014 - 8:01:23 PM

File

Li-NETCO2014.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01025882, version 1

Collections

Citation

Huijuan Li, Sigurđur Hafstein, Christopher M. Kellett. Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction. NETCO 2014 - New Trends in Optimal Control, Jun 2014, Tours, France. ⟨hal-01025882⟩

Share

Metrics

Record views

137

Files downloads

233