Regulation of discrete time linear systems with uncertain exosystems from noisy measurements

The class of discrete time, linear, reachable and observable systems with known parameters is considered: the regulation problem is addressed when the output channel is corrupted by additive unmodelled bounded noise not restricted to high frequencies and the input channel is affected by disturbances generated by a linear exosystem with unknown eigenvalues on the unit circle. A constructive robust algorithm is proposed to drive the system output exponentially into a set whose magnitude depends on the unmodelled noise magnitude. The control strategy includes an on-line estimator of the excited exosystem unknown parameters, whose observation error is shown to be rendered arbitrarily small by choosing a design parameter arbitrarily small; the output regulation error can also be rendered arbitrarily small, under standard regularity hypotheses, if the system to be regulated is asymptotically stable. The algorithm is tested on a numerical example to illustrate its effectiveness.