Dynamics of Relay Systems with Hysteresis and Harmonic Perturbation


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Authors

  • Alexander Mikhailovich Kamachkin
  • Dmitriy Konstantinovich Potapov
  • Victoria Viktorovna Yevstafyeva

Keywords:

multidimensional system of ordinary differential equations, relay hysteresis, harmonic perturbation, decomposition, parametric matrix, subsystems, Jordan block, asymptotically stable periodic solution

Abstract

We consider a system of ordinary differential equations with a relay hysteresis and a harmonic perturbation. We propose an approach that allows one to decompose an n-dimensional system into one- and two-dimensional subsystems. The approach is illustrated by a numerical example for the system of dimension 3. As a result of the decomposition, a two-dimensional subsystem with non-trivial Jordan block in right-hand side is studied. For this subsystem we prove a theorem on the existence and uniqueness of an asymptotically stable solution with a period being multiple to period of the perturbation. Moreover, we show how to obtain this solution by tuning the parameters defining the relay. We also provide a supporting example in this regard.

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Published

2024-07-15

How to Cite

Kamachkin, A. M., Potapov, D. K., & Yevstafyeva, V. V. (2024). Dynamics of Relay Systems with Hysteresis and Harmonic Perturbation. Eurasian Mathematical Journal, 15(2), 48–60. Retrieved from https://emj.enu.kz/index.php/main/article/view/342

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