Modelling switching power converters as complementarity systems

Switched complementarity models of linear circuits with ideal diodes and/or ideal switches allow one to study well-posedness and stability issues for these circuits by employing the complementarity problems of the mathematical programming. In this paper, we demonstrate that other types of typical electronic switching elements such as transistors and thyristors can also be treated in the framework of switched complementarity systems. By employing complementarity methods, we establish well-posedness results for a fairly large class of switched circuits that encompass power converters

On linear passive complementarity systems

We study the notion of passivity in the context ofcompleme ntaritysystems,whichformacl assofnonsmooth dynamical systems that is obtained from the coupling ofastandard input/output system to complementarity conditions as used in mathematical programming. In terms of electrical circuits, the systems that we study may be viewed as passive networks with ideal diodes. Extending results from earlier work, we consider here complementarity systemswithexternalinputs. Itisshownth attheassumption of passivity of the underlying input/output dynamical system plays an important role in establishing existence and uniqueness of solutions. We prove that solutions may contain delta functions but no higher-order impulses. Several characterizations are provided for the state jumps that may occur due to inconsistent initialization or to input discontinuities. Many of the results still hold when the assumption of passivity is replaced by the assumption of ``passifiability by pole shifting''. The paper ends with some remarks on stability

Computation of periodic solutions in maximal monotone dynamical systems with guaranteed consistency

\u3cp\u3eIn this paper, we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under some conditions. We discuss two numerical schemes based on time-stepping methods for the computation of the periodic solutions when these systems are periodically excited. We provide formal mathematical justifications for the numerical schemes in the sense of consistency, which means that the continuous-time interpolations of the numerical solutions converge to the continuous-time periodic solution when the discretization step vanishes. The two time-stepping methods are applied for the computation of the periodic solution exhibited by a power electronic converter and the corresponding methods are compared in terms of approximation accuracy and computation time.\u3c/p\u3

On the existence and uniqueness of solution trajectories to hybrid dynamical systems

In this paper, we study the fundamental system-theoretic property of wellposedness for several classes of hybrid dynamical systems. Hybrid systems are characterized by the presence and interaction of continu-ous dynamics and discrete actions. Many different description formats have been proposed in recent years for such systems; some proposed forms are quite direct, others lead to rather indirect descriptions. The more indirect a description form is, the harder it becomes to show that solutions are well-defined. This paper intends to provide a survey on the available results on existence and uniqueness of solutions for given initial conditions in the context of various description formats for hybrid systems

Modelling, well-posedness, and stability of switched electrical networks

A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. 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. 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 derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolv