Controllability and reachability criteria for discrete time positive systems.

*(English)*Zbl 0873.93009A discrete time positive system is described by the equation
\[
x(t+1)=Fx(t)+Gu(t)
\]
where \(x(t)\in R^n\) is the state vector, \(u(t) \in R^m\) is the input vector, and \(F\) and \(G\) are matrices of suitable dimensions, with nonnegative entries. In this class of systems the state variables are always nonnegative, starting from nonnegative initial states. In the paper in question a graph theoretic interpretation of controllability and reachability of discrete time positive systems is given, where controllability and reachability are to be understood both in ordinary and in “essential” sense, the last property being a weakening of the original one which arises in the context of positive systems. Necessary and sufficient conditions such that a given system is endowed with these properties are provided on the basis of a graph theoretic approach, together with canonical forms for describing reachable/controllable pairs.

Reviewer: E.De Santis (L’Aquila)