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We present a new synthesis solution for the state estimation problem of a class of discrete-time systems, namely linear systems up to Lipschitz nonlinearities. Our solution is obtained by using the Lipschitz condition jointly with the Lyapunov stability condition in order to guarantee the asymptotic stability of the estimation error. This result uses the linear matrix inequality (LMI) formulation.
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Bara et al. (2005) studied this question.