The problem of deadbeat state reconstruction for non-autonomous linear systems
has been solved since several decades, but all the architectures formulated since now require
either high-gain output injection, which amplifies measurement noises (e.g., in the case of
sliding-mode observers), either state augmentation, which yields a non-minimal realization of
the deadbeat observer (e.g., in the case of integral methods and delay-based methods). In this
context, the present paper presents, for the first time, a finite-time observer for continuous-time
linear systems enjoying minimal linear-time-varying dynamics, that is, the observer has the same
order of the observed system. The key idea behind the proposed method is the introduction of
an almost-always invertible time/output-dependent state mapping which allows to recast the
dynamics of the system in a new observer canonical form whose initial conditions are known.
