Absolute stability and integral control for infinite-dimensional discrete-time systems

We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input–output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l2l2-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input–output theory to state-space systems are also provided.