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Stability of Distributed Parameter Synchronization Systems with Disturbances

Vera Smirnova, Natalia Utina, Anton Proskurnikov
We examine stability properties of nonlinear systems with periodic nonlinearities, referred also to as synchronization systems or systems with cylindric phase space.
An important feature of such systems is their multistability: existence of infinite sequences of stable and unstable equilibria. An important problem regarding dynamics of such systems is the convergence of any solution to one of equilibria (asymptotic stability of the special attractor), referred to as the ``gradient-like behavior' or ``phase locking'.
Using the methods of absolute stability theory taking their origins in the works of V.M. Popov, new frequency-domain criteria for phase locking in synchronization systems are derived.
Unlike the existing results, we consider synchronization systems with distributed parameters and disturbances.
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