Stability of Dithered Feedback System Whose Nonlinearity Exhibits Hysteresis

We study the effects of dither on the nonlinear element of a SISO nonlinear feedback system. He consider nonlinearities with memory (hysteresis, backlash), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system. stability guarantees that of the given hysteretic system.