Journal of Dynamical and Control Systems

, Volume 23, Issue 4, pp 825–837 | Cite as

On Uniqueness and Properties of Periodic Solution of Second-Order Nonautonomous System with Discontinuous Nonlinearity

  • Alexander M. Kamachkin
  • Dmitriy K. PotapovEmail author
  • Victoria V. Yevstafyeva


We consider an automatic control system with discontinuous nonlinearity of non-ideal relay type and continuous external periodic influence. The control object can be either stable or unstable. In both cases, theorems on sufficient conditions for the existence of a unique periodic solution with given properties are obtained.


Discontinuous hysteresis nonlinearity Sinusoidal external influence Periodic solution Switching points Stability 

Mathematics Subject Classification (2010)

34A34 34A36 34H05 93C73 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Alexander M. Kamachkin
    • 1
  • Dmitriy K. Potapov
    • 1
  • Victoria V. Yevstafyeva
    • 1
  1. 1.Saint Petersburg State UniversitySt. PetersburgRussia

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