Output regulation for linear systems via adaptive. internal model

Given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear stable exosystem with unknown parameters and known order, the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered. The system is assumed to be known while the frequencies of the exosystem are unknown; all exosystem oscillatory modes are assumed to be excited by the initial condition. A global solution is proposed consisting of a dynamic output feedback controller which includes exponentially convergent estimates of the unknown frequencies.