Stability analysis of nonlinear power electronic systems utilizing periodicity and introducing auxiliary state vector

Octavian Dranga, Balázs Buti, István Nagy, Hirohito Funato

Research output: Contribution to journalArticle

26 Citations (Scopus)


Variable-structure piecewise-linear nonlinear dynamic feedback systems emerge frequently in power electronics. This paper is concerned with the stability analysis of these systems. Although it applies the usual well-known and widely used approach, namely, the eigenvalues of the Jacobian matrix of the Poincaré map function belonging to a fixed point of the system to ascertain the stability, this paper offers two contributions for simplification as well that utilize the periodicity of the structure or configuration sequence and apply an alternative simpler and faster method for the determination of the Jacobian matrix. The new method works with differences of state variables rather than derivatives of the Poincaré map function (PMF) and offers geometric interpretations for each step. The determination of the derivates of PMF is not needed. A key element is the introduction of the so-called auxiliary state vector for preserving the switching instant belonging to the periodic steady-state unchanged even after the small deviations of the system orbit around the fixed point. In addition, the application of the method is illustrated on a resonant dc-dc buck converter.

Original languageEnglish
Pages (from-to)168-178
Number of pages11
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number1
Publication statusPublished - Jan 1 2005



  • DC-DC power conversion
  • Nonlinear systems
  • Stability
  • Variable-structure systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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