基于离散时间观测与异步切换的周期性间断反馈控制对高非线性混合随机微分延迟方程的稳定性研究
Stabilization of highly nonlinear hybrid stochastic differential delay equations by periodically intermittent feedback controls based on discrete-time observations with asynchronous switching
AI总结：
本文研究高非线性混合随机微分延迟方程的矩指数稳定性，设计基于离散时间观测与异步切换的周期性间断控制器，确定观测周期上界和控制宽度下界，证明控制系统的指数稳定性及收敛速度。
摘要：
本文研究高非线性混合随机微分延迟方程的矩指数稳定性。设计基于离散时间状态观测与异步切换的周期性间断控制器，确定观测周期上界和控制宽度下界。首先在广义Khasminskii型条件下建立解的p阶矩有限性和有界性。然后提出合理的控制函数、漂移系数和扩散系数条件。接着证明受控系统的指数稳定性及收敛速度。最后通过实例说明控制区间比例与收敛速度正相关。
英文摘要：
In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous switching is designed. The upper bound of observation period as well as the lower bound of the control width are all obtained. Firstly, the finiteness and boundedness of the $p$-th moment of the solution are established under a generalized Khasminskii-type condition. Then reasonable conditions of control function, drift and diffusion coefficients are presented. Then exponential stability as well as the convergence rate of controlled system are proved. Finally, an example is presented to interpret the conclusion, which also indicates that the proportion of control interval has positive relation to the convergence rate.
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