State Space for Time Varying Delay

Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 423)

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.

Keywords

State Space Delay System Functional Differential Equation Reachability Condition Large Delay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA

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