Dynamics of Relay Systems with Hysteresis and Harmonic Perturbation
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Keywords:
multidimensional system of ordinary differential equations, relay hysteresis, harmonic perturbation, decomposition, parametric matrix, subsystems, Jordan block, asymptotically stable periodic solutionAbstract
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.