Computation of Lyapunov functions for discrete-time switched linear systems: Proof of convergence in the plane

Sigurdur F. Hafstein; Juan Javier Palacios Roman

doi:10.1016/j.ifacol.2025.11.097

Computation of Lyapunov functions for discrete-time switched linear systems: Proof of convergence in the plane

Sigurdur F. Hafstein
, Juan Javier Palacios Roman

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Onderzoeksoutput: Bijdrage aan tijdschrift › Congresartikel › peer review

1 Citaat (Scopus)

14 Downloads (Pure)

Samenvatting

Recently a novel method was presented to compute convex Lyapunov functions for discrete-time, switched linear systems. The method uses linear programming to parameterize continuous, cone-wise linear, convex Lyapunov functions. We prove that for two-dimensional systems the method is always able to generate a Lyapunov function, whenever the origin is exponentially stable, given that the triangulation used by the algorithm is sufficiently dense.

Originele taal-2	Engels
Pagina's (van-tot)	579-584
Aantal pagina's	6
Tijdschrift	IFAC-PapersOnLine
Volume	59
Nummer van het tijdschrift	19
DOI's	https://doi.org/10.1016/j.ifacol.2025.11.097
Status	Gepubliceerd - 1 jul. 2025
Evenement	13th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2025 - University of Iceland, Reykjavik, IJsland Duur: 23 jul. 2025 → 25 jul. 2025 Congresnummer: 13

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Publisher Copyright:
© 2025 The Authors. This is an open access article under the CC BY-NC-ND license.

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This work was supported in part by the Icelandic Research Fund under Grant 228725-051.

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abstract = "Recently a novel method was presented to compute convex Lyapunov functions for discrete-time, switched linear systems. The method uses linear programming to parameterize continuous, cone-wise linear, convex Lyapunov functions. We prove that for two-dimensional systems the method is always able to generate a Lyapunov function, whenever the origin is exponentially stable, given that the triangulation used by the algorithm is sufficiently dense.",

keywords = "discrete-time systems, linear programming, Lyapunov functions, switched systems",

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AB - Recently a novel method was presented to compute convex Lyapunov functions for discrete-time, switched linear systems. The method uses linear programming to parameterize continuous, cone-wise linear, convex Lyapunov functions. We prove that for two-dimensional systems the method is always able to generate a Lyapunov function, whenever the origin is exponentially stable, given that the triangulation used by the algorithm is sufficiently dense.

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Computation of Lyapunov functions for discrete-time switched linear systems: Proof of convergence in the plane

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Bibliografische nota

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