Stability theory and existence of periodic solutions of time delayed compartmental systems

This paper discusses the global asymptotic stability and existence of periodic solutions of periodically varying nonlinear compartmental systems with time delay. We exploit the inherent property that any bounded solution approaches a periodic solution. Based on this result, we derive a necessary and sufficient condition for a homogeneous (zero-input) system to be globally asymptotically stable and derive a necessary and sufficient condition for the system forced by a periodic input to admit a periodic solution. These conditions do not include time delay and are stated in terms of the interconnections among compartments. This amounts to showing that such qualitative properties of solutions are preserved irrespective of the introduction of arbitrary time delay.