Nonlinear Dynamics

, Volume 82, Issue 1–2, pp 563–575 | Cite as

New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

  • L. V. HienEmail author
  • V. N. Phat
  • H. Trinh
Original Paper


In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.


Generalized Halanay inequalities Exponential stability Non-autonomous systems Functional differential equations Time-varying delays 

Mathematics Subject Classification

34K20 49J30 93D15 



The authors would like to thank the Editor-in-Chief, Associate Editor(s) and Anonymous Reviewers for their valuable and encouraging comments and helpful suggestions to improve the present paper. This work was partially supported by the ARC Discovery (Grant DP130101532) and the NAFOSTED of Vietnam (Grant 101.01-2014.35).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam
  2. 2.Institute of MathematicsVASTHanoiVietnam
  3. 3.School of EngineeringDeakin UniversityGeelongAustralia

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