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Reachability and controllability of compartmental systems.

James G., Rumchev V.

Systems Science

2000

Vol. 26, nr 1

5-13

Compartmental models are frequently used in biology and medicine to analyze the behaviour of complex physiological systems and some of their properties (equilibrium points, stability, predicting the impact of different inflows) are well studied. Attempts have also been made to understand reachability and controllability properties of such models by employing the tests for linear systems. Linear compartmental systems as positive systems belong to the class of constrained linear systems, which are actually non-linear, and hence the reason why the general reachability and controllability tests developed for linear systems are fallible. In the paper, reachability and controllability properties of compartmental systems are studied by using some results in controllability theory for positive linear system. In particular, positive reachability and controllability criteria are in a digraph form, most suitable to the commonly used digraph representation of compartmental systems. Some specific compartmental models are also considered. The results obtained in the paper increase not only our understanding of the properties of compartmental models but they are also important for implementing feedback and optimal control strategies.