Discrete-time low-gain control of linear systems with input/output nonlinearities

Discrete-time low-gain control strategies are presented for tracking of con stant reference signals for finite-dimensional, discrete-time, power-stable , single-input, single-output, linear systems subject to a globally Lipschi tz, non-decreasing input nonlinearity and a locally Lipschitz, non-decreasi ng, affinely sector-bounded output nonlinearity (the conditions on the outp ut nonlinearities may be relaxed if the input nonlinearity is bounded). Bot h non-adaptive and adaptive gain sequences are considered. In particular, i t is shown that applying error feedback using a discrete-time 'integral' co ntroller ensures asymptotic tracking of constant reference signals, provide d that (a) the steady-state gain of the linear part of the plant is positiv e, (b) the positive gain sequence is ultimately sufficiently small and (c) the reference value is feasible in a very natural sense. The classes of inp ut and output nonlinearities under consideration contain standard nonlinear ities important in control engineering such as saturation and deadzone. The discrete-time results are applied in the development of sampled-data low-g ain control strategies for finite-dimensional, continuous-time, exponential ly stable, linear systems with input and output nonlinearities. Copyright ( C) 2001 John Wiley & Sons, Ltd.