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M. Arcak and D. Nesic, "A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation," Automatica, vol. 40, no. 11, pp. 1931-1938, Nov. 2004.
We study observer design for sampled-data nonlinear systems using two approaches: (i) the observer is designed via an approximate discrete-time model of the plant; (ii) the observer is designed based on the continuous-time plant model and then discretized for sampled-data implementation (emulation). We investigate under what conditions, and in what sense, these designs achieve convergence for the unknown exact discrete-time model. We present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model.