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Necessary and sufficient conditions for existence of estimators and controllers meeting desired H∞ performance criterion are given for the case where the finite sensor delays exist. A complete characterization of such controllers is also presented. The necessary and sufficient conditions are computable and are framed in terms of two algebraic Riccati equations and one finite-horizon Riccati differential equation. The controllers and estimators that are obtained here have a linear periodic structure and are easily implementable. At the foundation of these results lies a modified Nehari problem, the state space solution for which may be of independent interest.