Low-gain integral control of well-posed linear infinite-dimensional systems with input and output nonlinearities

Time-varying low-gain integral control strategies are presented for asympto tic tracking of constant reference signals in the context of exponentially stable, well-posed, linear, infinite-dimensional, single-input-single-outpu t, systems-subject to globally Lipschitz, nondecreasing input and output no nlinearities. It is shown that applying error feedback using an integral co ntroller ensures that the tracking error is small in a certain sense, provi ded that (a) the steady-state gain of the linear part of the system is posi tive, (b) the reference value r is feasible in an entirely natural sense, a nd (c) the positive gain function t --> k(t) is ultimately sufficiently sma ll and not of class L-1. Under a weak restriction on the initial data it is shown that (a), (b), and (c) ensure asymptotic tracking. If, additionally, the impulse response of the linear part of the system is a finite signed B orel measure, the global Lipschitz assumption on the output nonlinearity ma y be considerably relaxed. (C) 2001 Academic Press.