Robust H-infinity filtering for a class of nonlinear discrete time-delay systems with parameter uncertainties

Robust H-infinity filtering for a class of nonlinear discrete time-delay systems with parameter uncertainties is considered. The uncertainties are in a fractional form and the nonlinearities satisfy Lipschitz condition. The objective is the design of a full-order filer which guarantees not only the robust asymptotic-stability but also a prescribed disturbance attenuation level for the error system, irrespective of the parameter uncertainties. For systems without parameter uncertainties, a generalized bounded real lemma is first introduced, then sufficient conditions for the existence of H-infinity filters are derived. It is shown that the existence of H-infinity filters can be reduced to the solvability of linear matrix inequalities. Methods of designing H-infinity filters are provided in a framework of linear matrix inequalities. As for uncertain systems, the robust H-infinity filtering problem can be solved in terms of a scaled H-infinity filtering problem without uncertainties. Finally a numerical example is given to illustrate the effectiveness of the obtained results.