Abstract This paper is concerned with the problems of stochastic stability and control design for singular Markovian jump systems (SMJSs) with time varying delay. The derivative coefficient is considered to be mode dependent. A parameter-dependent reciprocally convex matrix inequality (PDRCMI) is constructed, which covers some existing ones as its special cases. Different from some existing ones, the introduced parameters are completely known, which can be optimized by an iteration algorithm. To decrease the redundant decision variables, a mild assumption is given for the case of mode-dependent coefficient such that the considered system is decomposed into differential equations and algebraic ones. In this case, the components of state vectors of the subsystem are applied to construct a new augmented Lyapunov-Krasovkii functional (LKF). Based on the PDRCI and the new augmented LKF, a novel stochastic stability condition with both less computational demands and less conservativeness is derived. Based on the decomposed subsystems and the stability condition, a set of state feedback controller is designed in terms of linear matrix inequalities (LMIs). Some numerical examples are introduced to illustrate the effectiveness of the proposed results.

中文翻译：

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基于参数相关的互逆凸矩阵不等式奇异马尔可夫跳跃系统的稳定性分析与控制设计

摘要 本文研究具有时变延迟的奇异马尔可夫跳跃系统(SMJS)的随机稳定性和控制设计问题。导数系数被认为是模式相关的。构造了一个依赖于参数的互反凸矩阵不等式（PDRCMI），它涵盖了一些现有的特殊情况。与现有的一些不同，引入的参数是完全已知的，可以通过迭代算法进行优化。为了减少冗余的决策变量，对模态相关系数的情况给出了一个温和的假设，以便将所考虑的系统分解为微分方程和代数方程。在这种情况下，子系统的状态向量组件被应用于构造一个新的增强 Lyapunov-Krasovkii 泛函 (LKF)。基于 PDRCI 和新的增广 LKF，推导出一种新的具有较少计算需求和较少保守性的随机稳定性条件。基于分解的子系统和稳定性条件，根据线性矩阵不等式(LMI)设计了一套状态反馈控制器。引入了一些数值例子来说明所提出结果的有效性。