On the reachability of discrete‐time compartmental systems with nonnegative input constraints

This paper investigates the properties of reachable sets of discrete‐time compartmental systems. The discrete‐time compartmental system is characterized by the non‐negativeness of all coefficients of its system state equations and its inputs. The paper first deals with the properties of reachable sets at finite sampling times of general ordinary linear discrete‐time systems with simple non‐negative input, and the n.a.s.c. under which the reachable set coincides with the maximal reachable set at finite sampling times. Then, it deals with the characteristic polynomial representation of state transition matrix and the properties of the maximal reachable set. After showing the properties of reachable sets of compartmental systems, the paper discusses the drug kinetics problem as an example of the analysis of reachable sets.