H∞ filtering of nonlinear sampled-data systems with parameter uncertainties

This paper considers the problem of nonlinear H_∞ filtering for sampled-data systems with nonlinear time-varying parameter uncertainty. The objective is to design a dynamic filter such that the ratio between the energy of the estimation errors and the energy of the exogenous inputs is minimized or guaranteed to be less or equal to a prescribed value for all admissible uncertainties. The connection between the robust nonlinear H_∞ filtering and the nonlinear H_∞ filtering problem for sampled-data system without uncertainty has been established. This connection enables us to solve the robust H_∞ filtering problem via recently developed nonlinear H_∞ filtering technique in terms of both continuous and discrete Hamilton-Jacobi equations