Compensators of the Ishlinskii hysteresis nonlinearities (Q1594196)

This article deals with elementary properties of compensator for the Ishlinskii classical hysteresis nonlinearity described by the operator \[ V[t_0, x_0(h); F]u(t)= \int^L_0 u_h[t_0, x_0(h)] u(t),\;dF(h) \] (\(U_h[t_0, x_0]u(\cdot)\) is a transducer-stop operator). The main results of the article are the explicit description of a compensator \(V[t_0, z_0(h);\Phi]\) for \(V[t_0, x_0(h); F]\), the theorem about general reciprocal invertibility of \(V[t_0, x_0(h); F]\) and \(V[t_0, z_0(h); \Phi]\) and some estimates for these operators.