Exponential tracking of general references and rejection of general disturbances for nonlinear control systems with applications to the blood glucose regulation system

In solving the problem of exponential tracking and disturbance rejection, it has been long always assumed that the reference to be tracked and the disturbance to be rejected are generated by an exosystem such as a finite dimensional system with pure imaginary eigenvalues. The aim of this note is to show that this assumption can be removed. For any nonlinear control system subject to a general disturbance, it can be split into a linear exponentially-stable system and a dynamical regulator system. If the dynamical regulator system has a solution, then there exists a feedback and feedforward controller such that an output of the control system exponentially tracks a desired general reference. The result is applied to the blood glucose regulation system.