This article is intended to deal with the problem of asynchronous admissibility and fault detection (FD) for time-varying delay implicit Markovian switching systems (IMSSs) under hidden Markovian model (HMM) mechanism. The fundamental purpose is to design asynchronous FD filter such that the implicit Markovian switching residual system is stochastically admissible (including regular, impulse-free, and stochastically stable) and satisfies the performance index. By constructing mode-dependent and delay-dependent Lyapunov–Krasovskii functional, improved conditions of asynchronous FD filtering are proposed in terms of linear matrix inequalities. The retarded mode-dependent time-varying delay is considered in this work when coping with admissibility of IMSSs, asynchronous FD for IMSSs is realized by virtue of designing asynchronous filter under HMM mechanism and fault weighting strategy. Simulation examples including an oil catalytic cracking process with multicycle incipient fault are provided to corroborate the validity and usefulness of the addressed asynchronous FD technique.

中文翻译：

---

隐马尔可夫模型机制下延迟隐马尔可夫切换系统的异步可容许性和故障检测

本文旨在处理隐马尔可夫模型（HMM）机制下时变延迟隐式马尔可夫交换系统（IMSS）的异步接纳和故障检测（FD）问题。其根本目的是设计异步FD滤波器，使得隐马尔可夫切换残差系统是随机允许的（包括规则的、无脉冲的和随机稳定的）并满足性能指标。通过构造依赖于模态和依赖于时延的 Lyapunov-Krasovskii 泛函，在线性矩阵不等式方面提出了异步 FD 滤波的改进条件。本工作在处理IMSS的可容许性时考虑了延迟模式相关的时变延迟，通过设计HMM机制下的异步滤波器和故障加权策略，实现了IMSS的异步FD 。模拟实例包括具有多循环初始故障的石油催化裂化过程，以证实所提到的异步 FD 技术的有效性和有用性。