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Complementarity: limit cycles and power converters


The research activity is dedicated to the analysis of the complemenatity framework for:

  • modeling of switched electronic systems (power converters, in particular)

  • computation of steady state solutions in switched systems and limit cycles in Lur'e systems


  • Kanat Camlibel, University of Groningen, The Netherlands


The classic approaches for modeling and simulating power converters (averaged, switched and hybrid models) and the commercial tools available (e.g. PSpice, Power System Blockset in the Matlab environment, PLECS) often do not allow the analysis of non-standard innovative converter topologies or operating conditions. The problem is tackled by using the complementarity systems theory. The complementarity approach, coming from the nonsmooth mechanics, allows to model the electronic devices by using piecewise affine characteristics, and then integrating them with detailed models of the converter and the network. The complementarity framework allows the formal and simulation analysis of innovative power converters topologies and electrical networks in terms of dynamic performance, failure and fault conditions, high frequency phenomena, switching behavior of the converters, frequency domain response.  Further, the complementarity approach with respect to simulation tools based on standard hybrid models, it also allows to gain in terms of simulation time and numerical convergence.

A similar approach to that used for the computation of steady state solutions for switched electronic systems can be used for the computation of limit cycles in Lur'e systems. It can be shown that the complementarity representation of the feedback characteristic allows to represent the discretized closed loop system as a linear complementarity system. A static linear complementarity problem, whose solutions correspond to periodic solutions of the discrete–time system, can then be formulated. The proposed technique is able to compute steady state oscillations with known period for continuous–time systems, so as demonstrated by simulation results on Lur’e systems which exhibit asymmetric unstable and sliding limit cycles.

PhD Theses

  • ongoing
    • Valentina Sessa, PhD student in Automatic Control, University of Sannio, "Limit cycles computation via complementarity models", co-tutor prof. Luigi Iannelli.
  • 2011
    • Gianluca Angelone, PhD in Automatic Control, University of Sannio, "Steady-state analysis for switched electronic systems through complementarity", co-tutor prof. Luigi Iannelli.

  • 2007
    • Roberto Frasca, PhD in Automatic Control, University of Sannio, "Modeling and simulation of switched electrical networks: A complementarity systems approach", co-tutor prof. Luigi Iannelli.

Laurea Magistralis Theses

  • 2011
    1. Maurizio Zoppi, LS Ingegneria dell'Automazione, ottobre 2011, "Complementary model and minimum energy control for switched capacitor converters", 110 e lode, co-relatore ing. Gianluca Angelone.