Output regulation for linear systems with anti-stable eigenvalues in the presence of input saturation

This paper studies the problem of output regulation for linear systems subject to input saturation. It is assumed that the dynamic matrix has anti-stable eigenvalues, that the disturbances affecting the plant are constant, sinusoidal or generically periodic signals with zero mean and that only the output of the plant is available for feedback. It is shown that the use of nonlinear controllers sensibly enlarge-with respect to what can be obtained using a linear dynamic feedback-the set of initial conditions (of the plant and the exosystem) for which the problem is solvable. An explicit expression of this set is also given.