Relationships between the reachability of positive standard and fractional discrete-time and continuous-time linear systems

Abstract

The relationships between the reachability of positive standard and fractional discrete-time and continuous-time linear systems are addressed. It is shown that: 1) The fractional positive discrete-time and linear systems are reachable in one step if and only if the corresponding positive standard system is reachable in one step; 2) If the positive standard discrete-time linear system with single input is unreachable, then the corresponding fractional positive system is also unreachable; 3) The fractional positive continuous-time linear system is reachable if and only if the corresponding continuous-time positive standard system is reachable.