Journal of Systems Science and Complexity

, Volume 19, Issue 2, pp 149–156

Stability of N-Dimensional Linear Systems with Multiple Delays and Application to Synchronization


DOI: 10.1007/s11424-006-0149-6

Cite this article as:
Deng, W., Lü, J. & Li, C. Jrl Syst Sci & Complex (2006) 19: 149. doi:10.1007/s11424-006-0149-6


This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore (2002). Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua’s systems.

Key Word

Chaos synchronizationmulti-delay linear systemsstability

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouChina
  2. 2.Department of MathematicsShanghai UniversityShanghaiChina
  3. 3.Key Laboratory of Systems and Control, Institute of Systems ScienceAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina
  4. 4.Department of Ecology and Evolutionary BiologyPrinceton UniversityUSA