Positive State Controllability of Discrete Linear Time-Invariant Systems

Positive state controllability is the controllability of systems where the state is positive and the input remains in ℝⁿ. Under some conditions, we established a relation between the reachability map of systems with only the positive state and the reachability map of a related positive system where the state and input are both positive. Using this connection, necessary and sufficient conditions are obtained for the positive state reachability of discrete linear time-invariant (LTI) systems, and then we deduced the positive state controllability. These conditions are evaluated over some numerical examples that support the theoretical results.