Robust filtering for a class of discrete-time uncertain nonlinear systems: AnH∞ approach

This paper deals with the H∞ filtering problem for a class of discrete-time nonlinear systems with or without real time-varying parameter uncertainty and unknown initial state. For the case when there is no parametric uncertainty in the system, we are concerned with designing a nonlinear H∞ filter such that the induced l2 norm of the mapping from the noise signal to the estimation error is within a specified bound. It is shown that this problem can be solved via one Riccati equation. We also consider the design of nonlinear filters which guarantee a prescribed H∞ performance in the presence of parametric uncertainties. In this situation, a solution is obtained in terms of two Riccati equations.