A Deadbeat Observer for Two and Three-dimensional LTI Systems by a Time/Output-Dependent State Mapping

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.