Set-Valued Observer Design for a Class of Uncertain Linear Systems with Persistent Disturbance

In this paper, a class of linear systems affected by both parameter variations and additive disturbances is considered. The problem of designing a set-valued state observer, which estimates a region containing the real state for each time being, 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 exponentially converges to a given compact set with an assigned rate of convergence.