On the non-linear discrete-time observer design problem

A set of conditions is presented, under which a non-linear discrete-time observer inducing linear estimation error dynamics exists for non-linear continuous (C0) discrete-time systems. In particular, the existence of a homeomorphism in state space is established that maps the orbits of a linear system with an output injection term onto the observing system, implying the existence of an invariant attracting manifold for the extended system. Within the aforementioned framework, it is shown that the discrete-time version of the Hartman-Grobman Theorem can be naturally reproduced as a special case. Finally, the performance of the proposed non-linear discrete-time observer is evaluated in two representative case studies, where two different dynamical systems of the Lozi and H?non-type are considered that exhibit non-linear and chaotic behaviour.

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