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Asynchronous Hybrid \(H_\infty \) Filtering for Uncertain Impulsive Switched Systems

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Abstract

This article addresses the hybrid \(H_\infty \) filtering problem for continuous-time uncertain linear impulsive switched systems with the asynchronous switching. Unlike most work about filtering problems, this article ponders multiple state impulsive jumps in the whole switched systems. In other words, the state impulsive jumps take place in subsystem switching instants as well as in filter switching instants, which add challenges to the \(H_\infty \) filtering problem considered in this article. In the filter design, one has to take account of the asynchronous switching, which hints that the switching of the subsystem and its corresponding filter does not occur concurrently. The average dwell time approach is applied to design the switching rule. This article focuses on the design of the hybrid \(H_\infty \) filter that can keep the filtering error systems globally uniformly asymptotically stable with \(H_\infty \) performance index. By constructing Lyapunov-like functions that allow the increment during the asynchronous period and in the state jump instants, sufficient conditions for the expected hybrid \(H_\infty \) filter are obtained in the form of linear matrix inequalities. At last, an example is offered to demonstrate the applications of the acquired theorems.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices (Grant no. JCKJ2022A05), the Natural Science Research Project of Colleges and Universities of Anhui Province (Grant no. 2023AH040123), and the National Natural Science Foundation of China (Grant nos. 61803001,61963010).

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Authors and Affiliations

  1. Anhui Key Laboratory of Detection Technology and Energy Saving Devices, Anhui Polytechnic University, Wuhu, People’s Republic of China

    Yufei Zhu, Xinya Mao & Qunxian Zheng

  2. School of Electrical Engineering, Anhui Polytechnic University, Wuhu, 241000, Anhui, People’s Republic of China

    Yufei Zhu, Xinya Mao & Qunxian Zheng

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Zhu, Y., Mao, X. & Zheng, Q. Asynchronous Hybrid \(H_\infty \) Filtering for Uncertain Impulsive Switched Systems. Circuits Syst Signal Process 43, 1392–1413 (2024). https://doi.org/10.1007/s00034-023-02533-w

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