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The problem of designing controllers for systems with delays, such that the closed-loop system is positive, stable and fulfils bounds on the system variables, is studied. In order to design this type of controller, a technique is provided, which is based on solving linear programming problems, as this allows the controllers that fulfil these properties to be easily characterised even in the presence of uncertainty in the plant description. Thus, these controllers ensure that the states are kept non-negative and that they fulfil limitations on the control and states. The work is completed with numerical simulations of the application of the methodology for router congestion control in computer networks, based on the synthesis of an active queue management system, thus demonstrating the usefulness of the proposed technique for practical problems.