On conditions of oscillations and multi-homogeneity

  • Denis Efimov
  • Wilfrid Perruquetti
Original Article


The notion of homogeneity in the bi-limit from Andrieu et al. (SIAM J Control Optim 47(4):1814–1850, 2008) is extended to local homogeneity and then to homogeneity in the multi-limit. The converse Lyapunov/Chetaev theorems on (homogeneous) system instability are obtained. The problem of oscillation detection for nonlinear systems is addressed. The sufficient conditions of oscillation existence for systems homogeneous in the multi-limit are formulated. The proposed approach estimates the number of oscillating modes and the regions of their location. Efficiency of the technique is demonstrated on several examples.


Nonlinear systems Homogeneity Instability Oscillations 


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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Non-A teamInria, Parc Scientifique de la Haute BorneVilleneuve d’AscqFrance
  2. 2.CRIStAL (UMR-CNRS 9189)Ecole Centrale de LilleVilleneuve-d’AscqFrance
  3. 3.Department of Control Systems and InformaticsUniversity ITMOSaint PetersburgRussia

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