具有正则脉冲矩的扰动拟线性系统的不可预测性
Unpredictability in Perturbed Quasilinear Systems with Regular Moments of Impulses
摘要：
严格证明了当不可预测序列产生扰动时，拟线性脉冲系统具有不可预测解。证明了解的存在唯一性和渐近稳定性。所考虑的系统是有规律的时刻的脉冲，并为此提供了一个新的定义不可预测的功能，定期不连续的时刻。利用分段连续函数的Gronwall型不等式来证明不可预测解的存在性。理论结果与一个说明性的例子支持。
英文摘要：
It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of such solutions are demonstrated. The system under consideration is with regular moments of impulses, and for that reason a novel definition for unpredictable functions with regular discontinuity moments is provided. To show the existence of an unpredictable solution a Gronwall type inequality for piecewise continuous functions is utilized. The theoretical results are supported with an illustrative example.
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