A survey of reachability and controllability for positive linear systems

This paper is a survey of reachability and controllability results for disc rete-time positive linear systems. It presents a variety of criteria in bot h algebraic and digraph forms for recognising these fundamental system prop el ties with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control, manpower planni ng, scheduling and other areas of operations research) but also in studying properties of reachable sets, in feedback control problems, and others. Th e paper highlights the intrinsic combinatorial structure of reachable/contr ollable positive linear systems and reveals the monomial components of such systems. The system matrix decomposition into monomial components is demon strated by solving some illustrative examples.