State space for time varying delay

Abstract

The construction of a state space for systems with time variant delay is analyzed. We show that under causality and consistency constraints a state space can be derived, but fails if the conditions are not satisfied. We rederive a known result on spectral reachability using an discretization approach followed by taking limits. It is also shown that when a system with fixed delay is modeled as one in a class with larger delay, reachability can no longer be preserved. This has repercussions in modeling systems with bounded time varying delay by embedding them in the class of delay systems with fixed delay, equal to the maximum of the delay function τ(t), or by using lossless causalization. © 2012 Springer-Verlag GmbH Berlin Heidelberg.