INPUT-TO-STATE STABILITY OF IMPULSIVE SYSTEMS WITH HYBRID DELAYED IMPULSE EFFECTS

Haitao Zhu; Peng Li; Xiaodi Li

doi:10.11948/2156-907X.20180182

2019 Volume 9 Issue 2

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Haitao Zhu, Peng Li, Xiaodi Li. INPUT-TO-STATE STABILITY OF IMPULSIVE SYSTEMS WITH HYBRID DELAYED IMPULSE EFFECTS[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 777-795. doi: 10.11948/2156-907X.20180182

Citation:

Haitao Zhu, Peng Li, Xiaodi Li. INPUT-TO-STATE STABILITY OF IMPULSIVE SYSTEMS WITH HYBRID DELAYED IMPULSE EFFECTS[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 777-795. doi: 10.11948/2156-907X.20180182

INPUT-TO-STATE STABILITY OF IMPULSIVE SYSTEMS WITH HYBRID DELAYED IMPULSE EFFECTS

1.
School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, China
2.
Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, School of Physics and Electronics, Shandong Normal University, Ji'nan, 250014, China

Corresponding author: Email address: lxd@sdnu.edu.cn (X. Li)
Fund Project: This work was supported by National Natural Science Foundation of China (61673247), and the Research Fund for Distinguished Young Scholars and Excellent Young Scholars of Shandong Province (JQ201719, ZR2016JL024). The paper has not been presented at any conference

Abstract

Abstract

The goal of this paper is to study properties of input-to-state stability $ (ISS) $ and integral input-to-state stability $ (iISS) $ of impulsive systems with hybrid delayed impulses, and a set of Lyapunov-based sufficient conditions ensuring $ ISS/iISS $ properties are obtained. Those conditions reveal the effects of hybrid delayed impulses on $ ISS/iISS $ and establish the relationship between impulsive frequency and the time delay existing in hybrid impulses. When the continuous dynamics of the system are stabilizing, the $ ISS $ property can be retained under the impulse scheme even if there exist destabilizing impulses. Conversely, when the impulse dynamics are stabilizing, but the continuous dynamics are not, the $ ISS $ property can be obtained if the interval between impulses are not overly long. Two illustrative examples are presented, with their numerical simulations, to demonstrate the effectiveness of the main results.
- Impulsive systems /
- hybrid delayed impulses /
- input-to-state stability (ISS) /
- integral input-to-state stability (iISS) /
- Lyapunov method
MSC: 37C75, 34A37

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References

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