Switched networks and complementarity
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KünyeÇAMLIBEL, M.K. HEEMELS, W.P.M.H., VAN DER SCHAFT, A.J. SCHUMACHER, J.M. (2003). Switched networks and complementarity. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Volume 50, Issue 8, pp. 1036 - 1046. http://dx.doi.org/10.1109/TCSI.2003.815195
A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this.