This paper deals with the problem of state estimation for single-output linear systems. Under some structural properties of the system matrices it is possible to design a hybrid observer capable of estimating the state of the system exactly and in a finite time. Moreover, the proposed hybrid observer provides fixed-time convergence of the state estimation error, i.e. there exists a convergence time that is bounded and such a bound is independent of the initial estimation error. The robustness properties of the hybrid observer are analyzed for the linear system with unknown inputs, and the linear system with unknown inputs and parametric uncertainty. Some simulation results illustrate the effectiveness of the proposed hybrid observer. (C) 2017 Elsevier Ltd. All rights reserved.