Output Regulation for Linear Minimum Phase Systems With Unknown Order Exosystem

Under the assumption that the regulation error is the only feedback signal, it is shown how to design a global regulator capable of rejecting and/or tracking signals made of at most m sinusoidal terms with unknown frequencies, magnitudes, and phases for linear observable minimum phase systems. The asymptotic convergence of the tracking error to zero is guaranteed provided that an upper bound is known on the number of sinusoidal terms, even though the values of the unknown frequencies may not be recovered. Exponential convergence is achieved if all the exosystem frequencies are excited.