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Forced oscillations in control systems with hysteresis. (English. Russian original) Zbl 0906.93027
Dokl. Math. 53, No. 2, 312-315 (1996); translation from Dokl. Akad. Nauk 347, No. 4, 458-461 (1996).
The authors study problems of forced oscillations in systems with hysteresis nonlinearities satisfying asymptotic conditions of the Landesman-Lazer type. The main method is the evaluation of the index at infinity of the corresponding vector fields. The description of specific classes of hysteresis models satisfying these conditions is given, in particular hysterons with saturation and hysteresis models of the dry friction type are considered. For problems with parameter, conditions for the appearance of a bifurcation from infinity are presented.

MSC:
93C10 Nonlinear systems in control theory
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiń≠, Uryson, etc.)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces
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