In 2013, Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback control based on discrete-time state observations. In recent years, this study has been further developed while using a constant observation interval. However, time-varying observation frequencies have not been discussed for this study. Particularly for non-autonomous periodic systems, it's more sensible to consider the time-varying property and observe the system at periodic time-varying frequencies, in terms of control efficiency. This paper introduces a periodic observation interval sequence, and investigates how to stabilize a periodic SDE by feedback control based on periodic observations, in the sense that, the controlled system achieves $ L^p $-stability for $ p>1 $, almost sure asymptotic stability and $ p $th moment asymptotic stability for $ p \ge 2 $. This paper uses the Lyapunov method and inequalities to derive the theory. We also verify the existence of the observation interval sequence and explain how to calculate it. Finally, an illustrative example is given after a useful corollary. By considering the time-varying property of the system, we reduce the observation frequency dramatically and hence reduce the observational cost for control.

中文翻译：

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基于周期离散时间观测值的反馈控制的连续时间周期随机系统的渐近稳定

2013年，毛开始了基于离散时间状态观测值的反馈控制稳定连续时间混合随机微分方程（SDE）的研究。近年来，在使用恒定观察间隔的同时，这项研究得到了进一步发展。但是，时变观测频率尚未对此研究进行讨论。特别是对于非自治周期性系统，考虑到时变特性并从控制效率的角度来看，以周期性时变频率观察系统更为明智。本文介绍了周期观测间隔序列，并研究了如何通过基于周期观测的反馈控制来稳定周期SDE，从某种意义上说，受控系统在$ p> 1 $时达到$ L ^ p $-稳定性，几乎可以确定$ p \ ge 2 $的渐近稳定性和$ p $ th矩渐近稳定性。本文使用李雅普诺夫方法和不等式推导该理论。我们还将验证观察间隔序列的存在并解释如何计算它。最后，在一个有用的推论之后给出一个说明性的例子。通过考虑系统的时变特性，我们大大降低了观测频率，从而降低了观测的控制成本。