This paper studies the dissipative filtering of singular Markovian jump systems (SMJSs) with generally hybrid transition rates (GHTRs). The transition rates of the mode jumps are considered to be generally hybrid, which relax the traditional assumption in Markov jump systems that estimate errors must be completely symmetric. The introduced generally hybrid transition rates (GHTRs) make these systems more general and realistic. In order to deal with the GHTRs, a new approach named double-boundary approach is proposed. Then, a new integral inequality named Wirtinger-type free-matrix-based integral inequality (WFMII) is proposed to estimate Lyapunov-Krasovskii functional (LKF), in which some delay-product-type matrices are produced to fully link the relationship among time-varying delay and system states. Based on these ingredients, an explicit expression of the desired filter can be given to ensure the filtering error system to be stochastically admissible and strictly dissipative. The further examination to demonstrate the feasibility of the presented method is given by designing a filter of a two-loop circuit network.

本文研究了具有一般混合跃迁率 (GHTR) 的奇异马尔可夫跳跃系统 (SMJS) 的耗散滤波。模式跳跃的转换率通常被认为是混合的，这放宽了马尔可夫跳跃系统中估计误差必须完全对称的传统假设。引入的一般混合转换率 (GHTR) 使这些系统更加通用和现实。为了处理GHTR，提出了一种称为双边界方法的新方法。然后，提出了一种新的积分不等式，命名为 Wirtinger 型基于自由矩阵的积分不等式（WFMII）来估计 Lyapunov-Krasovskii 泛函（LKF），其中产生一些延迟积型矩阵来完全链接时间之间的关系。 - 不同的延迟和系统状态。基于这些成分，可以给出所需滤波器的显式表达式，以确保滤波误差系统是随机可容许的和严格耗散的。通过设计一个双回路电路网络的滤波器，进一步检验证明所提出方法的可行性。