Bifurcations in two-dimensional piecewise smooth maps-theory and applications in switching circuits

Banerjee, S. ; Ranjan, P. ; Grebogi, C. (2000) Bifurcations in two-dimensional piecewise smooth maps-theory and applications in switching circuits IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications, 47 (5). pp. 633-643. ISSN 1057-7122

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Official URL: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arn...

Related URL: http://dx.doi.org/10.1109/81.847870

Abstract

Recent investigations on the bifurcation behavior of power electronic DC-DC converters have revealed that most of the observed bifurcations do not belong to generic classes such as saddle-node, period doubling, or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state space. In this paper we present a systematic analysis of such bifurcations through a normal form: the piecewise linear approximation in the neighborhood of the border. We show that there can be many qualitatively different types of border collision bifurcations, depending on the parameters of the normal form. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. We then use this theoretical framework to explain the bifurcation behavior of the current programmed boost converter.

Item Type:Article
Source:Copyright of this article belongs to IEEE.
ID Code:81353
Deposited On:06 Feb 2012 04:10
Last Modified:06 Feb 2012 04:10

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