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Many systems, arising in electrical and electronic engineering are based oncontrolled phase synchronization of several periodic processes ("phasesynchronization" systems, or PSS). Typically such systems are featured by thegradient-like behavior, i.e. the system has infinite sequence of equilibriapoints, and any solution converges to one of them. This property however saysnothing about the transient behavior of the system, whose important qualitativeindex is the maximal phase error. The synchronous regime of gradient-likesystem may be preceded by cycle slipping, i.e. the increase of the absolutephase error. Since the cycle slipping is considered to be undesired behavior ofPSSs, it is important to find efficient estimates for the number of slippedcycles. In the present paper, we address the problem of cycle-slipping forphase synchronization systems described by integro-differential Volterraequations with a small parameter at the higher derivative. New effectiveestimates for a number of slipped cycles are obtained by means of Popov'smethod of "a priori integral indices". The estimates are uniform with respectto the small parameter.

Estimation of transient process for singularly perturbed synchronization system with distributed parameters