This paper is concerned with the problem of robust H_∞ filtering for linear discrete-time systems with multiple state delays and polytopic uncertain parameters. Attention is focused on the design of full-order, reduced-order and zeroth-order robust H_∞ filters on the basis of a recently published parameter-dependent Lyapunov stability result. Sufficient conditions for the existence of such filters are formulated in terms of linear matrix inequalities, upon which admissible filters can be obtained from convex optimization problems. The proposed methodology has been shown, via a numerical example, to be much less conservative than previous filter design methods in the quadratic framework. This paper is concerned with the problem of robust H_∞ filtering for linear discrete-time systems with multiple state delays and polytopic uncertain parameters. Attention is focused on the design of full-order, reduced-order and zeroth-order robust H_∞ filters on the basis of a recently published parameter-dependent Lyapunov stability result. Sufficient conditions for the existence of such filters are formulated in terms of linear matrix inequalities, where which admissible filters can be obtained from convex optimization problems. a numerical example, to be much less conservative than previous filter design methods in the quadratic framework.