Time-Varying Linear Systems: Relative Degree and Normal Form

We define the relative degree of time-varying linear systems, show that it coincides with Isidori's and with Liberzon/Morse/Sontag's definition if the system is understood as a time-invariant nonlinear system, characterize it in terms of the system data and their derivatives, derive a normal form with respect to a time-varying linear coordinate transformation, and finally characterize the zero dynamics