Integral control in the presence of hysteresis: an input-output approach

Using an input-output approach, it is shown that under certain mild and natural assumptions, application of integral control to the series interconnection of a hysteretic input nonlinearity, an L²-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity guarantees tracking of constant reference signals, provided the positive time-dependent integrator gain is ultimately smaller than a certain constant determined by a positivity condition in the frequency domain. The input-output result is applied in a general state-space setting where in the linear component of the interconnection is given by a strongly stable well-posed infinite-dimensional system.