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Robustness of hybrid neutral differential systems perturbed by noise

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Abstract

This paper considers a given neutral functional system under regime switching whose solution grows at most polynomially. Can the system tolerate Brownian noise and colour noise to preserve the polynomial growth if the system is subject to another environment noise? The answer is positive. This paper shows that environmental noise and regime switching work together to make the original neutral differential system whose solution grows at most polynomially become a new neutral functional differential system whose solution will still preserve polynomial growth. This indicates that this neutral functional differential system can tolerate small noise without losing the property of polynomial growth, which implies robustness. This paper also proves that the criterion is suitable to neutral delay system which is as a special case of functional system. Finally, two examples are given to illustrate the main theory.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Shaobo Zhou & Fuke Wu

  2. School of Management, Huazhong University of Science and Technology, Wuhan, 430074, China

    Minggao Xue

Authors
  1. Shaobo Zhou
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  2. Minggao Xue
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  3. Fuke Wu
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Corresponding author

Correspondence to Minggao Xue.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 71471070, 61473125, 71171091, 11422110, and 11301198.

This paper was recommended for publication by Editor ZHANG Jifeng.

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Zhou, S., Xue, M. & Wu, F. Robustness of hybrid neutral differential systems perturbed by noise. J Syst Sci Complex 27, 1138–1157 (2014). https://doi.org/10.1007/s11424-014-2037-9

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  • DOI: https://doi.org/10.1007/s11424-014-2037-9

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