Feedback linearization of single-input control affine time-varying nonlinear systems

In this paper, we propose and solve the problem of feedback linearization of single-input control affine time-varying nonlinear systems. Feedback linearizability of time-varying is shown to be equivalent to the orbital feedback linearizability (or feedback linearization by state-dependent time scaling) of an extended version of the time-varying system. Necessary and sufficient conditions for feedback linearizability are presented. The conditions are simple and can be checked directly from the data of the problem. Using an exterior calculus approach, a simple algorithm is developed to compute state-dependent time scaling that yield state-feedback linearizable time-varying systems.