In this paper, almost sure exponential stabilization and destabilization criteria for nonlinear systems are obtained via aperiodically intermittent stochastic noises based on average techniques and piecewise continuous scalar functions. Compared with existing results on almost sure exponential stability of stochastic systems, the requirement on the upper bound of the diffusion operator of a Lyapunov function is released. The upper bound is allowed to be a scalar function and even be unbounded. Simultaneously, by means of putting forward new concepts “average noise control rate” and “average noise control period,” assumptions on infimum of control time and supremum of rest time in the previous references about aperiodically intermittent control can be removed without implementing in the upper limit of the uncontrolled rate, which reduces the conservativeness of stabilization criteria resulting from non-uniform distribution of control time and rest time. In addition, the main results are applied to coupled and uncoupled nonlinear spring–mass–damper oscillator systems, respectively, and corresponding numerical simulations are carried out to demonstrate the validity of the theoretical analysis.

中文翻译：

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通过非周期性间歇性随机噪声使非线性系统稳定和不稳定：平均技术和标量函数

在本文中，基于平均技术和分段连续标量函数，通过非周期性间歇性随机噪声，获得了几乎确定的非线性系统指数稳定和去稳定准则。与关于随机系统的几乎肯定的指数稳定性的现有结果相比，释放了对Lyapunov函数的扩散算子的上限的要求。上限允许为标量函数，甚至可以是无界的。同时，通过提出“平均噪声控制率”和“平均噪声控制周期”的新概念，可以消除先前参考文献中关于非周期性间歇控制的控制时间不足和静止时间最多的假设，而无需在上层实施。失控率的极限，这降低了由于控制时间和休息时间分配不均而导致的稳定标准的保守性。此外，主要结果分别应用于耦合和非耦合非线性弹簧-质量-阻尼器振荡器系统，并进行了相应的数值模拟，以证明理论分析的正确性。