Topics
Switching circuits are encountered in various applications from power converters to signal processing. To
simplify the analysis, the switching elements are typically taken as ideal elements. Such ideal switching behavior may cause: Collaborations  Cem Goknar, Dogus University, Istanbul Turkey
 Kanat Camlibel, Univeristy of Groningen, The Netherlands
 Stephan Trenn, University of Kaiserslautern, Germany
Abstract
For discontinuities in the state variables (typically voltages across capacitors and currents through inductors), a good deal of literature has been devoted to the problem of state reinitialization, i.e., determining the state after a discontinuity. We study the state reinitilization problem for electrical networks consisting of linear passive elements, independent voltage/current sources, and ideal switches. We employ the socalled 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, we introduce a new state reinitialization rule that is based on energy minimization at the time of switching. Inspired by nonlinear phenomena exhibited by power electronics converters, we study the classification of nonstandard bifurcations in piecewise smooth feedback systems. Bifurcations involving fixed points in maps, equilibria and limit cycles in flows are considered with particular attention to: border collisions of fixed points in maps; nonsmooth bifurcations of equilibria, grazing bifurcations and sliding bifurcations of limit cycles in flows. The aim is to describe existing and novel results to form the basis of a consistent theory of bifurcations in such systems. In so doing, a novel approach to classify nonsmooth bifurcations of equilibria in flows can be proposed.
PhD Theses
 ongoing
 Carmen Pedicini, PhD student in
Automatic Control, University of Sannio, "Averaging for switched systems", cotutor prof. Luigi
Iannelli.
 2007
 Roberto Frasca,
PhD in
Automatic Control, University of Sannio, "Modeling and simulation of
switched electrical networks: A complementarity systems approach",
cotutor prof.
Luigi Iannelli.
Laurea Magistralis Theses  2011
 Maurizio Zoppi,
LS Ingegneria dell'Automazione, ottobre 2011, "Complementary model and
minimum energy control for switched capacitor converters", 110 e lode,
corelatore ing. Gianluca Angelone.
Laurea Theses
 2012
 Giuliano Costantini, L Ingegneria Informatica, luglio 2012, "State jumps in electrical circuits", 110 e lode.
Publications
 2010
 R. Frasca, M. K. Camlibel, I. C. Goknar, L.
Iannelli, F. Vasca, "Linear Passive Networks with Ideal Switches: Consistent Initial Conditions and State Discontinuities", IEEE
Transactions on Circuits and Systems, vol. 57 , no. 12 , December 2010,
p. 31383151.
 2008
 R. Frasca, K. Camlibel , C. I. Goknar, L. Iannelli, F. Vasca, "State
Jump Rules in Linear Passive Networks with Ideal Switches and Sources",
IEEE International Symposium on Circuits and Systems, Seattle,
Washington, May 2008, p. 540543.
 2002
 M. di Bernardo, F.
Garofalo, L. Iannelli, F. Vasca, "Bifurcations in PiecewiseSmooth Feedback Systems", International Journal of Control, vol. 75, no. 16/17,
2002, p. 12431259.
 M. di Bernardo, K. H. Johansson, U. Jonsson, F.
Vasca, "On the Robustness of Periodic Solutions in Relay Feedback Systems", 15th IFAC World Congress, Barcelona, Spain, July 2002.
 M. di Bernardo, L.
Iannelli, F. Vasca, "Experimental Detection of Bifuractions and Sliding in DC/DC Power Converters", IEEE International Symposium on Circuits And
Systems, Phoenix, Arizona, vol. I, May 2002, p. 385388.
 2000
 M.
di Bernardo, F. Vasca, "Discrete Time Maps for the Analysis of Bifurcations and Chaos in DC/DC Converters", IEEE Transactions on
Circuits and Systems, Part I, vol. 47, no. 2, February 2000, p.130143.
 M. di Bernardo, K. H. Johansson, F.
Vasca, "Bifurcation and Symmetry in Relay Feedback Systems", Nonlinear
Dynamics of Electronic Systems, Catania, Italy, June 2000.
 1999
 M.
di Bernardo, K. H. Johansson, F. Vasca, "Sliding Orbits and Their
Bifurcations in Relay Feedback Systems", 38th IEEE Conference on
Decision and Control, Phoenix, Arizona, December 1999, p. 708713.
 M. di Bernardo, A. R. Champneys, C. J. Budd, F.
Vasca, "Sliding Orbits and Double Spiral Bifurcation Diagrams in Power
Electronics DC/DC Converters", IEEE International Symposium on Circuits
And Systems, Orlando, Florida, vol. V, May 1999, p. 262265.
 1998
 M.
di Bernardo, L. Glielmo, F. Garofalo, F. Vasca, "Switchings, Bifurcations and Chaos in DC/DC Converters", IEEE Transactions on
Circuits and Systems, Part I, vol. 45, no. 2, February 1998, p. 133141.
 1997
 M.
di Bernardo, E. Fossas, G. Olivar, F. Vasca, "Secondary Bifurcations and High Periodic Orbits in Voltage Controlled Buck Converter",
International Journal of Bifurcation and Chaos, vol. 7, no. 11, November
1997, p. 27552771.
 M.
di Bernardo, F. Garofalo, L. Glielmo, F. Vasca, "Analysis of Chaotic
Buck, Boost and BuckBoost Converters through Switching Maps", 28th IEEE
Power Electronics Specialists Conference, St. Louis, Missouri, June
1997, p. 754760.
 1996
 M. di Bernardo, F.
Garofalo, L. Glielmo, F. Vasca, "Nonlinear Phenomena in Pulse Width
Modulated Feedback Controlled Systems", 35th IEEE Conference on Decision
and Control, Kobe, Japan, December 1996, p. 21612166.
 M. di
Bernardo, F. Garofalo, L. Glielmo, F. Vasca, "QuasiPeriodic Behaviors
in DC/DC Converters", 27th IEEE Power Electronics Specialists
Conference, Baveno, Italy, June 1996, p. 13761381.
