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Sector estimates of nonlinearities and the existence of self-oscillations in control systems. (English. Russian original) Zbl 1056.34507
Autom. Remote Control 61, No. 6, Part 1, 889-903 (2000); translation from Avtom. Telemekh. 2000, No. 6, 3-18 (2000).
Summary: Simple conditions for the existence of nontrivial (nonequilibrium) periodic solutions of autonomous control systems are derived in terms of ordinary linear two-sided sector estimates on nonlinearities and linear asymptotics of nonlinearities at zero and infinity. The limiting bounds of sector estimates are determined by properties of the linear component. The designed methods yield two-sided estimates on the period of a cycle if the sector estimate is fixed.

MSC:
34C25 Periodic solutions to ordinary differential equations
34H05 Control problems involving ordinary differential equations
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