Set-point regulation of monotone systems using the monotone small-gain theorem

Monotone dynamical systems are those with solutions preserving specific orderings, relative to the associated initial states. This study shows that, under negative output feedback control, a monotone single-input single-output system with well-defined static characteristics is able to globally asymptotically regulate its solution at desired constant set-points, while the boundedness of all solutions are successfully guaranteed. This valuable result is obtained only through limited amount of qualitative and quantitative data, which may be provided from relatively simple experiments for real applications. The design procedure, in the cast of a new theorem, is mainly derived from the specific version of Small Gain Theorem for autonomous monotone systems; which ensures the global attractivity of the desired set-point. A biological simulation example illustrates the effectiveness and applicability of the proposed control strategy.