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Globally exponential stability of delayed impulsive functional differential systems with impulse time windows

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Abstract

In the practical application of impulsive differential systems, impulse does not always occur at the fixed-time point; it may occur in a little range of time. Namely, impulse occurs in a time window, which is more general and more nearing to reality than those fixed-time impulses. Therefore, it is necessary to investigate the dynamical behaviors of impulsive differential systems with impulse time windows. In this paper, the exponential stability of these systems is researched. By means of Lyapunov functions, Razumikhin technique and other analysis methods, several novel exponential stability criteria for delayed impulsive functional differential equations with impulse time windows are obtained, which are different from the previously published results for fixed-time impulses. What is more, based on the analysis of this paper, it is worth noting that choosing an efficient impulse time window may be easier and more effective than choosing fixed-time impulsive sequences. Finally, three examples and their simulations are provided to illustrate the effectiveness of our results.

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Acknowledgments

The work was supported by the National Natural Science Foundation of China (Grant Nos. 61372139, 61503175, 61571372, 61374078, 61101233, 60972155), Program for New Century Excellent Talents in University(Grant Nos.[2013]47), “Spring Sunshine Plan” Research Project of Ministry of Education of China (Grant No. z2011148), Fundamental Research Funds for the Central Universities (Grant Nos. XDJK 2016A001 and XDJK2014A009), Program for Excellent Talents in scientific and technological activities for Overseas Scholars, Ministry of Personnel in China (Grant No. 2012-186), University Excellent Talents Supporting Foundations in of Chongqing (Grant No. 2011-65), University Key Teacher Supporting Foundations of Chongqing (Grant No. 2011-65), High School Key Scientific Research Project of Henan Province (Grant No. 15A120013). This publication was made possible by NPRP grant \(\sharp \) NPRP 4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation).

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Authors and Affiliations

  1. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Huamin Wang, Shukai Duan, Chuandong Li & Lidan Wang

  2. Department of Mathematics, Luoyang Normal University, Luoyang, 471022, Henan, People’s Republic of China

    Huamin Wang

  3. Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Doha, 23874, Qatar

    Tingwen Huang

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  1. Huamin Wang
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  2. Shukai Duan
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  4. Lidan Wang
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Correspondence to Shukai Duan.

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Wang, H., Duan, S., Li, C. et al. Globally exponential stability of delayed impulsive functional differential systems with impulse time windows. Nonlinear Dyn 84, 1655–1665 (2016). https://doi.org/10.1007/s11071-015-2594-z

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  • DOI: https://doi.org/10.1007/s11071-015-2594-z

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