This paper extends the existing results on the robust H_∞ filtering problem for singular Markovian jump systems. Firstly, the double variables‐based decoupling principle and the variable substitution principle are proposed, respectively. Secondly, the two principles are employed to formulate a robust H_∞ filter design condition, which ensures the filtering error system to be stochastically admissible and meet H_∞ performance. Compared with the existing works, this paper fully considers the free structure of introduced slack matrices, which provides extra dimensions in the solution space. It directly leads to the reduction of conservativeness in the filtering solution. The effectiveness of the proposed methods is illustrated by a numerical example.

中文翻译：

---

基于去耦和替换原理的奇异马尔可夫跳跃系统的鲁棒H∞滤波

本文扩展，而对健壮的现有结果ħ _∞奇异马尔可夫跳变系统过滤问题。首先，分别提出了基于双变量的解耦原理和变量替代原理。其次，两个原则被用于制定鲁棒ħ _∞滤波器的设计条件，这确保了过滤误差系统是随机受理，并满足ħ _∞表现。与现有工作相比，本文充分考虑了引入的松弛矩阵的自由结构，该结构在解空间中提供了额外的维数。这直接导致过滤解决方案中的保守性降低。数值例子说明了所提出方法的有效性。