17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper MoA08.4

Eberard, Damien (Univ. of Lyon), Maschke, Bernhard (Univ. Claude Bernard de Lyon), van der Schaft, Arjan (Univ. of Groningen)

Energy-Conserving Formulation of RLC-Circuits with Linear Resistors

Scheduled for presentation during the Regular Session "Networks" (MoA08), Monday, July 24, 2006, 12:05−12:30, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 28, 2024

Keywords Algebraic and differential geometry, Networks and circuits, Passivity

Abstract

In this paper firstly, the dynamics of LC-circuits without excess elements is expressed in terms of contact systems encompassing in a single formulation the Hamiltonian formulation and the pseudo-gradient formulation called the Brayton-Moser equations. Indeed the contact formulation encompasses both the Hamiltonian system and its the adjoint variational system. Secondly we express the dynamics of RLC-circuits with linear resistors in the contact formalism by extending the state space to an associated space of Thermodynamic phase which again encompasses as well the Hamiltonian formulation with dissipation as the Brayton-Moser formulation.