On estimators for nonlinear systems in Lp spaces

Estimation problems are addressed for continuous-time, nonlinear dynamic systems in a general L_p framework. In this setting, the connection between the observation and the filtering problems is investigated. Under some regularity assumptions for the nonlinearities and suitable bounds on the L_p norm of the noises, it is proved that the same hypotheses sufficient to design an exponential observer for a system without noises enable one to design a filter which is L-stable with respect to system and measurement noises. An illustrative example is finally presented