In this paper, we study the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces. A set of sufficient conditions are established for controllability of nonlinear stochastic delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices. Furthermore, controllability results for second-order stochastic delay systems driven by Rosenblatt distributions via the representation of solution by delayed sine and cosine functions are presented. Finally, our theoretical results are illustrated through numerical simulation.

中文翻译：

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由 Rosenblatt 分布驱动的随机非线性振荡延迟系统的可控性

在本文中，我们研究了有限维空间中由 Rosenblatt 分布驱动的二阶非线性随机延迟系统的可控性。利用不动点理论、延迟的正余弦矩阵和延迟的格拉姆矩阵，建立了非线性随机延迟系统可控性的一组充分条件。此外，通过延迟正弦和余弦函数的解表示，给出了由 Rosenblatt 分布驱动的二阶随机延迟系统的可控性结果。最后，通过数值模拟说明了我们的理论结果。