This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection ofeither (a) a hysteretic input nonlinearity, an L 2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L 2-stable, time-invariantlinear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference signals, provided the positive integrator gain is smaller than a certainconstant determined by a positivity condition in the frequency domain. The input-output results are applied in a general state-space setting wherein the linear component of the interconnection is a well-posed infinite-dimensional system.

We derive absolute stability results of Popov-type for infinite-dimensional systems in an input-output setting. Our results apply to feedback systems where the linear part is the series interconnection of an $L^2$-stable linear system and an integrator, and the non-linearity satisfies a sector condition which allows for non-linearities with lower gain equal to zero (such as saturation, or more generally, bounded non-linearities). These results are used to prove convergence and stability properties of low-gain integral feedback control applied to $L^2$-stable linear systems subject to actuator and sensor non-linearities. The class of actuator/sensor non-linearities under consideration contains standard non-linearities which are important in control engineering such as saturation and deadzone. Moreover, we use the input-output theory developed to derive state-space results on absolute stability and low-gain integral control for strongly stable well-posed infinite-dimensional linear systems.

We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral feedback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone.