Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction

Huijuan Li; Sigurdur Hafstein; Christopher M. Kellett

doi:10.1109/CDC.2014.7040251

Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction

Huijuan Li
, Sigurdur Hafstein
, Christopher M. Kellett

Faculty of Physical Sciences

University of Iceland

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The proposed 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 converse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.

Original language	English
Article number	7040251
Pages (from-to)	5512-5517
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2015-February
Issue number	February
DOIs	https://doi.org/10.1109/CDC.2014.7040251
Publication status	Published - 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014

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10.1109/CDC.2014.7040251

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title = "Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction",

abstract = "In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The proposed 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 converse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.",

author = "Huijuan Li and Sigurdur Hafstein and Kellett, \{Christopher M.\}",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

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T1 - Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction

AU - Li, Huijuan

AU - Hafstein, Sigurdur

AU - Kellett, Christopher M.

PY - 2014

Y1 - 2014

N2 - In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The proposed 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 converse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.

AB - In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The proposed 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 converse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.

UR - https://www.scopus.com/pages/publications/84988268655

U2 - 10.1109/CDC.2014.7040251

DO - 10.1109/CDC.2014.7040251

M3 - Conference article

SN - 0743-1546

VL - 2015-February

SP - 5512

EP - 5517

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

IS - February

M1 - 7040251

T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014

Y2 - 15 December 2014 through 17 December 2014

ER -

Computation of Lyapunov functions for discrete-time systems using the Yoshizawa construction

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