Sampled-data low-gain integral control of linear systems with actuator and sensor nonlinearities

Non-adaptive (but possibly time-varying) and adaptive sampled-data low-gain integral control strategies are derived for asymptotic tracking of constant reference signals for exponentially stable, finite-dimensional, single-input, single-output, linear systems subject to a globally Lipschitz, nondecreasing actuator nonlinearity and a locally Lipschitz, nondecreasing, affinely sector-bounded sensor nonlinearity (the conditions on the sensor nonlinearities may be relaxed if the actuator nonlinearity is bounded). In particular, it is shown that applying error feedback using a sampled-data low-gain controller ensures asymptotic tracking of constant reference signals, provided that (a) the steady-state gain of the linear part of the continuous-time plant is positive, (b) the positive controller gain sequence is ultimately sufficiently small and not of class l 1 and (c) the reference value is feasible in a natural sense.