Triple Asynchronous Fault Detection for Fuzzy Semi-Markov Jump Systems

This paper investigates the problem of triple asynchronous event-triggered fault detection filtering for fuzzy semi-Markov jump systems. In practical applications, ensuring synchronous operation among the system, event generator and filter becomes challenging due to various factors such as interference and time delays. These factors complicate the coordination and performance of the system, especially when dealing with systems that operate in multiple modes. Moreover, the limited network resources present in real world scenarios further exacerbate the problem, necessitating the development of more efficient control and filtering schemes. To address these challenges, an asynchronous event-triggered scheme is proposed, along with a corresponding filter and premise variables asynchronous that are designed to handle the inherent delays and resource constraints. Two hidden semi-Markov models are introduced to describe the asynchronous phenomenon between plant, event generator and filter. Using Lyapunov stability theory, sufficient conditions are derived to guarantee that the system is not only stochastically stable and satisfies the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}_{\infty}$</tex> performance, but also ensures that the filter gains can be obtained. Finally, a modified DC motor equivalent circuit model is taken as an example to demonstrate the effectiveness of the proposed method.