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