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Event-Triggered \(H_{\infty }\) Filtering for Discrete-Time Markov Jump Systems with Repeated Scalar Nonlinearities

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Abstract

This paper is concerned with the \(H_{\infty }\) filtering problem for discrete-time Markov jump systems with repeated scalar nonlinearities in an event-triggered communication scheme. An event-triggered scheme is proposed to determine whether the current data should be transmitted to the filter or not. Based on the time interval analysis approach, the discrete-time Markov jump system with network-induced delays under event-triggered communication scheme is converted into the discrete-time Markov jump time-delay system. By employing the positive-definite diagonally-dominant-type Lyapunov function technique, criteria are derived to guarantee the system is stochastically stable with a prescribed \(H_{\infty }\) performance level. The correspondent filter and the event-triggered parameters are also solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (61803134) and the Zhejiang Provincial Natural Science Foundation of China (LZ17F030002, LY20F030011).

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Authors and Affiliations

  1. Fair Friend Institute of Intelligent Manufacturing, Hangzhou Vocational & Technical College, Hangzhou, 310018, China

    Huijiao Wang

  2. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou, 310018, China

    Huijiao Wang

  3. Nanhu College, Jiaxing University, Jiaxing, 314001, China

    Yujia Ying

  4. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou, 310018, China

    Anke Xue

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  1. Huijiao Wang
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  2. Yujia Ying
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  3. Anke Xue
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Correspondence to Huijiao Wang.

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Wang, H., Ying, Y. & Xue, A. Event-Triggered \(H_{\infty }\) Filtering for Discrete-Time Markov Jump Systems with Repeated Scalar Nonlinearities. Circuits Syst Signal Process 40, 669–690 (2021). https://doi.org/10.1007/s00034-020-01511-w

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