Robustness of hybrid neutral differential systems perturbed by noise
Robustness of hybrid neutral differential systems perturbed by noise
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DOI：
10.1007/s11424-014-2037-9
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发表时间：
2014-11
影响因子：
2.1
通讯作者：
Shaobo Zhou;Minggao Xue;Fuke Wu
中科院分区：
文献类型：
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作者：
Shaobo Zhou;Minggao Xue;Fuke Wu
本文考虑了一个给定的中立型泛函系统在区域切换下，其解至多多项式增长。如果系统受到另一种环境噪声的影响，系统能否容忍布朗噪声和色噪声以保持多项式增长？答案是肯定的。本文证明了环境噪声和状态转换的共同作用，使得原来的解最多多项式增长的中立型微分系统成为一个新的中立型泛函微分系统，其解仍然保持多项式增长。这表明，该中立型泛函微分系统可以容忍小噪声，而不会失去多项式增长的性质，这意味着鲁棒性。本文还证明了该判据适用于作为泛函系统特例的中立型时滞系统。最后，给出了两个例子来说明本文的主要理论.
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.