This paper deals with the control of processes having recycle streams. These processes can be modeled as state delayed systems. In this work the problem of robust design of an observed-based controller for these systems is presented. The system is assumed to have norm-bounded uncertainties which are independent in every matrix involved in its state space realization. To ensure asymptotic stability of the closed loop system, a Lyapunov functional is used to obtain delay-independent design conditions. The controller design is accomplished by means of a convex optimization procedure formulated using linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the main characteristics of the proposed design method.