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

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Road, Hanoi, Vietnam

    L. V. Hien

  2. Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, 10307, Vietnam

    V. N. Phat

  3. School of Engineering, Deakin University, Geelong, VIC, 3217, Australia

    H. Trinh

Authors
  1. L. V. Hien
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  2. V. N. Phat
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  3. H. Trinh
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Correspondence to L. V. Hien.

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Hien, L.V., Phat, V.N. & Trinh, H. New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems. Nonlinear Dyn 82, 563–575 (2015). https://doi.org/10.1007/s11071-015-2176-0

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  • DOI: https://doi.org/10.1007/s11071-015-2176-0

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