Controllability in Linear Sequential Networks

A linear sequential network (LSN) with m inputs and
n
delay elements can be viewed both as a linear control system and as a sequential machine. A linear system is
k
controllable if and only if every state transition can be achieved in exactly
k
steps. It is shown that controllability is equivalent to
n
controllability, and that a LSN is
n
controllable if and only if it is a stronglyconnected sequential machine. Techniques are given for determining controllability in LSN's, for finding a sequence of
n
input vectors for an arbitrary state transition, and for finding a similar sequence of
k
input vectors, where
k
is the smallest integer such that the LSN is
k
controllable.