A novel internal model-based tracking control for a class of linear time-varying systems

This paper provides a novel method of constructing an internal model-based design of reference tracking and/or disturbance rejection for a class of linear time-varying plants with a known linear time invariant (LTI) exosystem. It is shown how the realization of an appropriate time-varying internal model can be constructed by means of a novel feedback mechanism. The design of the internal model consists of two ingredients: (1) a timevarying system immersion of the exosystem, and (2) an automatic generation of the desired control input to render the error-zeroing subspace invariant, based on the complete knowledge of the plant model. The important features of the proposed method lie in that the tracking problem setup and the proposed feedback mechanism allow us to avoid explicitly calculating the desired input, which keeps the regulated error identically at zero. Moreover the time-varying immersion is guaranteed to hold for the class of plant models under consideration. These features significantly broaden the range of applications of the proposed method, and simplify the control implementation process.