In this paper we construct an infinite horizon minimax state observer for a linear stationary differentialalgebraic equation (DAE) with uncertain but bounded input and noisy output. We do not assume regularity or existence of a (unique) solution for any initial state of the DAE. Our approach is based on a generalization of Kalman's duality principle. In addition, we obtain a solution of infinite-horizon linear quadratic optimal control problem for DAE. © 2013 IEEE.