Varying time delay feedback has found wide applications in stabilization and controlling of nonlinear dynamic systems. It has been a challenging topic to analyze nonlinear systems with time delay feedback, especially when the delay is varying. Here in this paper an analytical criterion is deduced, according to which alternate stability switches can be determined for nonlinear oscillators equipped with fast varying periodic time delay feedback. The criterion renders an analytical boundary being given by a concise and explicit function in the parameter space of interest. The controlled Duffing and the Duffing–van der Pol oscillators are investigated by the presented criterion. Analytical results are in well consistence with the numerical ones obtained by the Runge–Kutta method. It reveals that the stability region depends on the amplitude of varying time delay, but not on the frequency as long as it is large enough.

时变反馈已在非线性动态系统的稳定和控制中得到了广泛的应用。分析具有时间延迟反馈的非线性系统是一个具有挑战性的话题，尤其是在延迟变化时。本文在此推导了一种分析标准，据此，可以为配备快速变化的周期性时滞反馈的非线性振荡器确定替代的稳定性开关。该标准提供了一个分析边界，该边界由目标参数空间中的简洁明了函数给出。通过提出的标准研究了受控Duffing和Duffing-van der Pol振荡器。分析结果与通过Runge-Kutta方法获得的数值非常吻合。