Applications of Mathematics, first online, pp. 1-16


Continuous dependence on parameters and boundedness of solutions to a hysteresis system

Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva

Received March 22, 2020.   Published online February 18, 2021.

Abstract:  We analyze an ordinary differential system with a hysteresis-relay nonlinearity in two cases when the system is autonomous or nonautonomous. Sufficient conditions for both the continuous dependence on the system parameters and the boundedness of the solutions to the system are obtained. We give a supporting example for the autonomous system.
Keywords:  ODE system; hysteresis relay; external disturbance; bounded solution; periodic solution
Classification MSC:  34C11, 34C25, 34C55, 93C15, 93C73
DOI:  10.21136/AM.2021.0085-20

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Affiliations:   Alexander M. Kamachkin, Dmitriy K. Potapov (corresponding author), Victoria V. Yevstafyeva, Saint Petersburg State University, 7/9, Universitetskaya nab., St. Petersburg, 199034, Russia, e-mail: a.kamachkin@spbu.ru, d.potapov@spbu.ru, v.evstafieva@spbu.ru


 
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