Equivalence of Linear Time-Delay Systems

The question of characterizing those time-delay systems which are equivalent (up to bicausal transformations) to a delay-free system is a natural and fundamental problem which has been raised since the early 1980s. Surprisingly, this problem remains largely open despite that some partial answers have been provided. This technical note tackles this problem for linear systems with constant time delays, and gives necessary and sufficient conditions to eliminate, whenever is possible, or to reduce the number of time delays and a constructive way to get the corresponding bicausal change of coordinates.