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Upper bounds for frequency of periodic regimes in many-dimensional and infinite dimensional phase synchronization systems

Vera Smirnova, Natalia Utina, Aleksey Perkin, Alexander Shepeljavyi
A lot of control systems arising in electrical engineering, electronics, mechanics and telecommunications may be modeled as interconnection of a linear plant, described by differential or integro–differential equations and a periodic nonlinear feedback. These mathematical models are often referred to as phase synchronization systems (PSS). Typically such systems are featured by the gradient–like behavior, i.e. any solution of the system converges to one of equilibrium points. If a PSS in not gradient-like it may have periodic regimes which are undesirable for most systems. In the present paper, we address the problem of lack or existence of periodic regimes for phase synchronization
systems with lumped and with distributed parameters. New effective frequency–algebraic estimates for the frequency of possible periodic regimes are obtained by means of Fourier expansions and the tool of Popov functionals destined specially for periodic nonlinearities.
CYBERNETICS AND PHYSICS, Vol. 4, No. 2. 2015, 41-48.
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