Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty

This paper deals with the problem of robust H X filtering for a class of state-delayed non-linear systems with normbounded parameter uncertainty appearing in all the matrices of the linear part of the system model. The non-linearities are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. Attention is focused on the design of a non-linear filter which ensures both the robust stability and a prescribed H X performance of the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expression of a desired H X filter is also presented. A numerical example is provided to demonstrate the applicability of the proposed approach.