Stabilization Under Constrained States and Controls of Positive Systems with Time Delays

This paper solves the stabilization problem for positive linear discrete-time systems subject to time-delays, under state and control constraints. The synthesis of statefeedback stabilizing controllers is solved in terms of Linear Programming. The proposed approach deals with the stabilization with bounded controls and states, in the presence of possibly unknown delays. Also, the robust control design is considered, and it is illustrated with an example from pharmacokinetics.