Linear Passive Networks With Ideal Switches: Consistent Initial Conditions and State Discontinuities

Abstract

This paper studies linear passive electrical networks with ideal switches. We employ the so-called linear switched systems framework in which these circuits can be analyzed for any given switch configuration. After providing a complete characterization of admissible inputs and consistent initial states with respect to a switch configuration, the paper introduces a new state reinitialization rule that is based on energy minimization at the time of switching. This new rule is proven to be equivalent to the classical methods of Laplace transform and charge/flux conservation principle. Also we illustrate the new rule on typical examples that have been treated in the literature.