  We study the possibility of nullifying time-varying systems with memoryless
output feedback. The systems we examine are linear single-input single-output
finite-dimensional time-varying systems. For generic completely controllable
and completely observable discrete-time systems, we show that any state at any
time can be steered to the origin within finite time. An algorithm for
nullification and an upper bound for nullification time, depending only on the
system's dimension, are provided. The algorithm is described using a
representation of the system in time-varying controller canonical form. We
verify that every completely controllable system has such a representation. The
application of the nullification algorithm to sampled-data systems is also
analysed: we show that a controllable continuous-time time-varying system with
analytic coefficients can be nullified utilising zero-hold sampling of the
output and time-varying memoryless linear feedback; for generic observables,
almost any sampling period can be used. We also prove that controllability of
time-varying systems with analytic coefficients is preserved under zero-hold
sampling at almost any rate.
