PF-stable estimators for nonlinear systems

摘要

The stability of filters for nonlinear dynamic systems with Lipschitz nonlinearities is addressed. By considering the disturbances in the system and measurement equations as the inputs to the system representing the estimation error dynamics, the input-output stability of the filtering mapping associated with the estimation error dynamics is introduced. This is done with respect to signals belonging a Sobolev space W. The connection between W-stability and asymptotic stability (based on the existence of a suitable Lyapunov function) of the filtering mapping is investigated.