Abstract In this paper, the design of finite-time mixed H ∞ and passive asynchronous filter for T–S fuzzy singular Markov jump systems with general transition rates under the dynamic event-based scheme is discussed. An asynchronous filter is considered such that the phenomena of asynchronous modes between the original singular Markov jump systems and the considered filter is modelled as a hidden Markov model. A dynamic event-based scheme is proposed to further mitigate the network transmission burden. By augmenting the states of the original singular Markov jump systems and the constructed asynchronous filter, the filtering error system is transformed into a singular time-delay Markov jump system. Based on the Lyapunov–Krasovskii functional concerning the internal dynamic variable, the criteria of stochastically admissible and stochastically finite-time boundness with the given mixed H ∞ and passivity performance index for the filtering error system are subject to linear matrix inequalities and several constraint conditions. Furthermore, the unified co-design approach of the desired asynchronous filter and the proposed dynamic event-based strategy is developed. Finally, a numerical instance is employed to demonstrate the correctness and effectiveness of the developed technique.

中文翻译：

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具有一般跃迁率的 T-S 模糊奇异马尔可夫跳跃系统的基于动态事件的有限时间混合 H∞ 和无源异步滤波

摘要 本文讨论了基于动态事件方案的具有一般跃迁率的T-S模糊奇异马尔可夫跳跃系统的有限时间混合H ∞ 和无源异步滤波器的设计。考虑异步滤波器，使得原始奇异马尔可夫跳跃系统和所考虑的滤波器之间的异步模式现象被建模为隐马尔可夫模型。提出了一种基于动态事件的方案，以进一步减轻网络传输负担。通过对原始奇异马尔可夫跳跃系统的状态进行增广和构造的异步滤波器，将滤波误差系统转化为奇异时滞马尔可夫跳跃系统。基于关于内部动态变量的 Lyapunov-Krasovskii 泛函，给定混合H ∞ 和滤波误差系统的无源性能指数的随机容许和随机有限时间有界准则受线性矩阵不等式和若干约束条件的约束。此外，开发了所需异步过滤器的统一协同设计方法和所提出的基于动态事件的策略。最后，通过一个数值实例来证明所开发技术的正确性和有效性。