Nonlinear Dynamics

, Volume 86, Issue 1, pp 153–163 | Cite as

Partial stability analysis of nonlinear nonstationary systems via averaging

  • A. Yu. Aleksandrov
  • E. B. Aleksandrova
  • Y. Chen
Original Paper


Certain classes of essentially nonlinear nonstationary systems are studied. With the aid of the Lyapunov direct method and the averaging technique, conditions are obtained under which the zero solutions of the considered systems are stable with respect to all variables and asymptotically stable with respect to a part of variables. It is shown that the proposed approach can be used for the stability analysis of equilibrium positions of nonlinear mechanical systems. Some examples are presented to demonstrate the effectiveness of our results.


Nonlinear systems Partial stability Lyapunov functions Nonstationary perturbations Averaging approach Mechanical systems 



The research was supported by the Saint Petersburg State University (Project No. 9.42.1041.2016), by the Russian Foundation for Basic Research (Grant No. 15-58-53017) and by the National Science Foundation of China (Project Nos. 6141101096, 61573030 and 64961273006).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • A. Yu. Aleksandrov
    • 1
  • E. B. Aleksandrova
    • 1
  • Y. Chen
    • 2
  1. 1.Saint Petersburg State UniversitySt. PetersburgRussia
  2. 2.College of Metropolitan TransportationBeijing University of TechnologyBeijingChina

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