Positivity and LTI systems

This paper investigates the external and internal positivity of standard linear systems, in which the input function is restricted to be positive. By using cone-invariant matrix operators, we find parametric conditions on a system such that its state is contained within a proper convex cone. Then, by use of the dual of said proper cone, we first establish sufficient conditions for external positivity. From this result, we find conditions for internal positivity based on the external positivity of an analog system. Lastly, we investigate internal positivity independently of its external counterpart.