Abstract
This paper considers a PBH test for reachability in a linear time-varying discrete-time systems. Let R denote the set of all real-valued functions defined on the set of integers. We consider a time-varying discrete-time system to be over R, and characterize the system in terms of a semilinear transformation. Mode-reachability is defined in terms of eigenvalues and eigenvectors of the semi-linear transformation. It is shown that mode-reachability is equivalent to Kalman's original reachability.
