This paper presents a comprehensive study addressing the problem of finite-time interval stabilization (FTIS) for two distinct types of systems: linear time-invariant stochastic delayed systems (LTISDSs) and linear time-varying stochastic delayed systems (LTVSDSs). To begin, the definition of FTIS is established, which is based on employing piecewise state feedback controllers. Subsequently, a time-varying Lyapunov-Krasovskii functional (LKF) is proposed and a novel optimization algorithm is designed to address the challenge of FTIS for LTISDSs. Additionally, this paper investigates the equivalence of LTVSDSs to uncertain stochastic delayed systems with interval parameters, represented as a series of convex combinations. Notably, both the optimization algorithm and the linear matrix inequalities (LMIs) technique are employed to establish sufficient conditions for achieving FTIS in LTVSDSs. Furthermore, when compared to traditional state feedback controllers, the piecewise controllers not only enhance the precision of system control but also lead to reduced control gains and fewer control effort requirements. Finally, the findings are substantiated through the presentation of two numerical examples, providing practical validation for the proposed methodologies and their effectiveness.

中文翻译：

---

分段控制器基于区间矩阵法的时变随机时滞系统的有限时间区间镇定

本文提出了一项综合研究，解决两种不同类型系统的有限时间间隔稳定（FTIS）问题：线性时不变随机延迟系统（LTISDS）和线性时变随机延迟系统（LTVSDS）。首先，建立 FTIS 的定义，该定义基于采用分段状态反馈控制器。随后，提出了时变 Lyapunov-Krasovskii 泛函（LKF），并设计了一种新颖的优化算法来解决 LTISDS 的 FTIS 挑战。此外，本文还研究了 LTVSDS 与具有区间参数（表示为一系列凸组合）的不确定随机时滞系统的等价性。值得注意的是，优化算法和线性矩阵不等式（LMI）技术都被用来为 LTVSDS 中实现 FTIS 建立充分的条件。此外，与传统的状态反馈控制器相比，分段控制器不仅提高了系统控制的精度，而且导致控制增益降低和控制工作量要求减少。最后，通过两个数值例子证实了研究结果，为所提出的方法及其有效性提供了实际验证。