In this paper, we propose a deadbeat state observer
for LTI systems having the same dimension of the
observed system and with no discontinuous high-gain injection.
An invertible time/output dependent coordinate transformation
is introduced to convert the original system to a so-named
deadbeat observer canonical form, which is endowed with the key
property of having known initial conditions. A state observer is
then designed for the transformed system, providing deadbeat
convergence of the estimates in the ideal case. Remarkably, in
presence of noisy input and output signals, the estimation error
is proved to be ISS with respect to the measurement noise and
its bound is characterized theoretically. Numerical simulations
are carried out to examine the effectiveness of the proposed
observer in comparison with an existing finite-time method.
