Abstract
Positive systems appear naturally in economics, biology, biochemistry, where the variables take only nonnegative values. The paper discusses positive reachability of nonlinear discrete-time positive systems. Various sufficient conditions and necessary conditions of positive reachability and local positive reachability are derived. The role of axial reachability, which is necessary for positive reachability, is investigated. The results on positive reachability for discrete-time systems and continuous-time systems are compared. Positive reachability of continuous-time systems is much more demanding. This leads to the conclusion that Euler type discretization of locally positively reachable continuous-time system results in a locally positively reachable discrete-time system.
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