Necessary and sufficient conditions for bounded control of positive systems

This paper addresses the bounded control of positive systems, both continuous- and discrete-time ones. The control is under boundedness constraint, which means that both the input and the states of the closed-loop system are bounded and positive (the original systems are not necessarily positive). The main contribution lies in two aspects. First, a necessary and sufficient condition is provided for the bounded control of continuous-time systems. Second, a similar condition is also established for the discrete-time systems. All the controllers are explicitly constructed if existent and all the results are formulated as linear programming problems, hence easy to be verified.