Reachability and controllability of positive linear discrete-time systems with time-delays

Many practical systems in engineering, management science, economics, social sciences, compartmental analysis in biology and medicine, can be modelled as positive systems in which the state trajectory is always positive whenever the initial state is positive. This paper first introduces the time-delay phenomenon into positive linear discrete-time systems and studies reachability and controllability of such systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is also shown that for time-delay positive systems, reachability and null controllability together imply complete controllability.