Robust stabilization of positive linear systems via sliding positive control

In this paper a robust control is proposed for a family of positive and compartmental systems. Sufficient conditions are provided for the stabilization of this kind of systems by using sliding mode theory. The construction of a stabilizing hyperplane with a sliding dynamics is detailed and the feasibility of the method is discussed. The method is illustrated with three examples. The first one is a two-dimensional system which is used only to show the details about the computation, the construction of the stabilizing hyperplane and the robustness of the control. Complementary, the last two are actual interesting cases of biomedical systems and they show potential applications about the stabilization and closed-loop performance. It should be noted that these biomedical systems arise as a current class of dynamical systems with interesting challenges for the process control.