Stabilization of Linear Systems with Time-Varying Delays

  • Jing ZhuEmail author
  • Tian Qi
  • Dan Ma
  • Jie Chen
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 8)


In this chapter, we extend the preceding stabilization results to linear systems with time-varying delays. The extension is rendered possible by the operator-theoretic approaches developed in Chaps.  3 and  4: While the small-gain stability conditions are developed in Chap.  3 for systems with time-varying delays, the interpolation approach used in Chap.  4 enables us to address stabilization problems directly based on the small-gain conditions. This insures that the results on the delay margin can be cohesively extended, and in a unified manner. Indeed, it will be seen that bulk of the results in Chap.  4 can be used to address the stabilization of systems with time-varying delays, modulo to some minor modifications. Efficient computational formulas and analytical expressions are also obtained, which incorporate the time-varying delay characteristics of delay range and delay variation rate.

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Center for Control and OptimizationSouth China University of TechnologyGuangzhouChina
  3. 3.College of Information Science and EngineeringNortheastern UniversityShenyangChina
  4. 4.Department of Electronic EngineeringCity University of Hong KongHong KongHong Kong

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