  This paper is motivated by a class of positive systems with an input that is
subject to an unknown state-dependent power law delay as well as saturation.
For example, biological networks have non-negative protein concentration
states. Mass action kinetics in these systems result in power law behavior,
while complex interactions cause signal propagation delays. Incomplete network
characterization makes delay state-dependence unknown. Manipulating network
activity via modulated protein concentrations to attain desired performance is
restricted by upper-bounds on concentration actuator authority. Here, an
innovative control law exploits system dynamics to compensate for control
domain restrictions. A Lyapunov stability analysis establishes that the
reference tracking error of the closed-loop system is uniformly ultimately
bounded. Numerical simulations on a human coagulation model show controller
efficacy and better performance compared to the relevant literature. This
example application steps toward personalized, closed-loop treatments for
trauma coagulopathy, which currently has 30% mortality with open-loop clinical
approaches.
