In this paper, a class of linear systems affected by parameter variations, additive noise and persistent disturbances is considered. The problem of designing a set-valued state observer, which estimates a region containing the real state for each time instant, is investigated. The techniques for designing the observer are based on positive invariant set theory. By constructing a set-induced Lyapunov function, it is shown that the estimation error converges exponentially to a given compact set with an assigned rate of convergence.