This article focus on the robust H_∞ stability analysis and controller design for a class of uncertain and disturbed continuous-time systems with input time-varying delays characterized by stochastic Bernoulli distributions. First, robust H_∞ stability conditions for linear continuous systems with interval input time-varying delays is investigated. A delay-distribution-approach is considered to reduce the conservatism of the stability conditions from the convenient selection of a Lyapunov–Krasovskii functional (LKF), which considers both the lower and upper bounds of the stochastic time-varying delay to derive new delay-dependent H_∞ stability conditions in terms of linear matrix inequalities (LMIs). Then, derived from the proposed stability conditions, LMI-based conditions for the design of stabilizing robust H_∞ delayed state feedback controller are proposed. Finally, five numerical examples are considered to show the effectiveness of the proposed stability analysis and controller design conditions, in comparison to previous related results.

中文翻译：

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改进的鲁棒 H∞ 稳定性分析和具有随机输入时变延迟的不确定系统的稳定性

本文重点讨论一类不确定和受干扰的连续时间系统的鲁棒H _∞稳定性分析和控制器设计，该系统具有以随机伯努利分布为特征的输入时变延迟。首先，研究了具有间隔输入时变延迟的线性连续系统的鲁棒H _∞稳定性条件。考虑到随机时变延迟的下限和上限以推导出新的延迟-相关H _∞线性矩阵不等式 (LMI) 方面的稳定性条件。然后，根据所提出的稳定性条件，提出了用于设计稳定鲁棒H _∞延迟状态反馈控制器的基于 LMI 的条件。最后，与以前的相关结果相比，五个数值例子被认为是表明所提出的稳定性分析和控制器设计条件的有效性。