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.