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This paper investigates the problem of asymptotic state observation for analytic nonlinear discrete-time systems. A new technique for the observer construction, based on the Taylor polynomial approximation of the inverse of the observability map, is presented and discussed. The degree chosen for the approximation is the most important design parameter of the observer, in that it can be chosen such to ensure the convergence of the observation error at any desired exponential rate, in any prescribed convergence region (semiglobal exponential convergence).

A Discrete-time Observer Based on the Polynomial Approximation of the Inverse Observability Map