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Invariant convex classes of states of continual relay systems. (English. Russian original) Zbl 0854.93028
Autom. Remote Control 55, No. 10, Pt. 1, 1405-1412 (1994); translation from Avtom. Telemekh. 1994, No. 10, 17-26 (1994).
A large class of admissible states is generally inconvenient for studying free and forced periodic oscillations in systems described by ordinary differential equations or evolution equations of mathematical physics. In this paper, taking narrower classes of states having additional special properties and using operator methods, it is possible to construct nonlinear completely continuous operators whose fixed points define the periodic solutions of evolution problems with hysteresis.

93B28 Operator-theoretic methods
93C10 Nonlinear systems in control theory
93A99 General systems theory