Lyapunov stability analysis of networks of scalar conservation laws

2007, Volume 2, Issue 4: 751-759. doi: 10.3934/nhm.2007.2.751

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1.
Center for Systems Engineering and Applied Mechanics (CESAME), Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve
2.
Center for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve
3.
Département de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405, Orsay
4.
Centre de Robotique (CAOR), Ecole nationale supérieure des mines de Paris, 60, Boulevard Saint Michel, 75272 Paris Cedex 06

It is shown how an entropy-based Lyapunov function can be used for the stability analysis of equilibria in networks of scalar conservation laws. The analysis gives a sufficient stability condition which is weaker than the condition which was previously known in the literature. Various extensions and generalisations are briefly discussed. The approach is illustrated with an application to ramp-metering control of road traffic networks.
- Lyapunov stability,
- conservation laws,
- physical networks
Citation: Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws[J]. Networks and Heterogeneous Media, 2007, 2(4): 751-759. doi: 10.3934/nhm.2007.2.751

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Abstract

It is shown how an entropy-based Lyapunov function can be used for the stability analysis of equilibria in networks of scalar conservation laws. The analysis gives a sufficient stability condition which is weaker than the condition which was previously known in the literature. Various extensions and generalisations are briefly discussed. The approach is illustrated with an application to ramp-metering control of road traffic networks.
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© 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)