A Deadbeat Observer for LTI Systems: a Time/Output-Dependent State Mapping

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.