Low-gain integral control of continuous-time linear systems subject to input and output nonlinearities

Abstract

Continuous-time low-gain integral control strategies are presented for tracking of constant reference signals for finite-dimensional, continuous-time, asymptotically stable, single-input single-output, linear systems subject to a globally Lipschitz and non-decreasing input nonlinearity and a locally Lipschitz, non-decreasing and affinely sector-bounded output nonlinearity. Both non-adaptive (but possibly time varying) and adaptive integrator gains are considered. In particular, it is shown that applying error feedback using an integral controller ensures asymptotic tracking of constant reference signals, provided that (a) the steady-state gain of the linear part of the plant is positive, (b) the positive integrator gain is ultimately sufficiently small and (c) the reference value is feasible in a very natural sense. The classes of actuator and sensor nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone.