On the linear regulator with unknown stable exosystems

Given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear exosystem with unknown parameters and unknown order, the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered. The linear system to be regulated is allowed to be a non-minimum phase: its parameters are required to be known. Only an upper bound on the number of the excited frequencies of the exosystem is assumed to be known. A global solution is proposed, which includes asymptotically convergent estimates of the excited unknown frequencies.