Memorizing properties of hysteresis media. (English. Russian original) Zbl 1058.47509

Vladimirov, A. A.

Autom. Remote Control 58, No. 12, Part 1, 1886-1899 (1997); translation from Avtom. Telemekh. 1997, No. 12, 18-34 (1997).

Summary: A hysteresis nonlinearity is regarded as an input-output correspondence, continuous in the uniform metric and invariant with respect to monotone changes of time. A class of hysteresis nonlinearities is said to separate two inputs if there exists a nonlinearity in this class such that the corresponding outputs are different at some finite time. We find a simple class of “elementary” hysteresis nonlinearities with scalar inputs and outputs and a two-dimensional state space that separates any pair of inputs that are not equivalent to each other with respect to monotone changes of time. Realization theorems proved in the paper substantiate the possibility of approximation of scalar hysteresis operators by special combinations of elementary hysteresis nonlinearities.

MSC:

47N70	Applications of operator theory in systems, signals, circuits, and control theory
47J40	Equations with nonlinear hysteresis operators
47H30	Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
34C55	Hysteresis for ordinary differential equations
93A30	Mathematical modelling of systems (MSC2010)

Keywords:

scalar operators; uniform approximation; causality; extended states; controllability; hysteresis operators