A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based nonlinear observer design approach is presented, which guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of random perturbations, due possibly to computational errors or changes during operation, on the observer gain. Some simulation examples are included to illustrate the proposed design methodology.

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