Reachability and Observability Graphs for Linear Positive Systems on Time Scales?

Abstract: Positive reachability and positive observability of positive linear systems on time scales are studied. Differential and integral calculus on time scales allows for unified treatment of continuous- and discrete-time systems. Reachability and observability graphs for positive systems are introduced. They are used to characterize positive reachability and positive observability for systems on homogeneous time scales. It is also shown that positive observability is dual to positive reachability. Positive minimality is introduced and characterized with the aid of Gram matrices, Hankel matrices and graphs