TY - JOUR
T1 - Switched Networks and Complementarity
AU - Camlibel, Mehmet
AU - Heemels, W.P.M.H.
AU - van der Schaft, A.J.
AU - Schumacher, J.M.
N1 - Relation: http://www.rug.nl/informatica/onderzoek/bernoulli
Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
PY - 2003
Y1 - 2003
N2 - 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 cover also 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.
AB - 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 cover also 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.
KW - piecewise-linear systems
KW - ideal switches
KW - ideal diodes
KW - hybrid systems
KW - complementarity systems
M3 - Article
SN - 1057-7122
VL - 50
SP - 3036
EP - 1046
JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
ER -