SIAM Journal on Control and Optimization, Volume 58, Issue 5, Page 2900-2926, January 2020.
For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems. Response lags are required by most physical systems and play a key role in the feedback control. The aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching diffusion system (SDS) to be exponentially stable in the $p$th moment with probability one as well as stable in $H_\infty$. The designed control principles are implementable to stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the criteria are sharp that under the control with high strength the controlled SDSs will be stable (bounded) while under the weaker control they will be unstable (unbounded) in the mean square. The sample and moment Lyapunov exponents are estimated which have a close relationship to the time delays.

中文翻译：

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基于离散观测的切换扩散系统的延迟反馈控制

SIAM控制与优化杂志，第58卷，第5期，第2900-2926页，2020年1月。
为了节省时间和成本，基于离散时间观测的反馈控制用于稳定开关扩散系统。大多数物理系统都需要响应滞后，并且在反馈控制中起关键作用。本文的目的是基于系统状态和马尔可夫状态的离散时间观测值来设计延迟反馈控制功能，以使受控开关扩散系统（SDS）在$ p $ th矩下具有指数稳定性。以及$ H_ \ infty $中的稳定率。设计的控制原理可以实现，以稳定准线性和高度非线性的SDS。对于准线性SDS，标准是严格的，即在强度较高的控制下，受控SDS在稳定度上将是稳定的（有界），而在较弱的控制下，它们的均方值将是不稳定的（无界）。估计了样本和矩李雅普诺夫指数，它们与时间延迟密切相关。