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Computation of Lyapunov Functions for Discrete-Time Systems using the Yoshizawa Construction

Abstract : In this paper, we present a new approach for com-puting Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The pro-posed method constructs a continuous piecewise affine (CPA) function on a compact subset of the state space containing the origin, given a suitable triangulation or partition of the compact set and values at the vertices of the triangulation. Here, the vertex values are fixed using a function from a classical con-verse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.
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https://hal.inria.fr/hal-01101289
Contributor : Estelle Bouzat <>
Submitted on : Friday, March 6, 2015 - 8:18:09 PM
Last modification on : Friday, August 23, 2019 - 3:08:02 PM
Long-term archiving on: : Sunday, June 7, 2015 - 10:05:56 AM

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  • HAL Id : hal-01101289, version 1

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Huijuan Li, Sigurður Hafstein, Christopher M. Kellett. Computation of Lyapunov Functions for Discrete-Time Systems using the Yoshizawa Construction. CDC 2014, Dec 2014, Los Angeles, United States. ⟨hal-01101289⟩

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