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Generalized non-fragile asynchronous mixed \(H_\infty \) and passive output tracking control for neutral Markov jump systems

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Abstract

This paper dealt with the problem of output tracking for neutral Markov jump systems with multiple delays based on generalized non-fragile asynchronous feedback control. Attention is focused on the design of generalized non-fragile asynchronous feedback controller to ensure that the closed-loop system is stochastically stabilization and meet an expected mixed \( H_\infty \) and passivity performance index. The modes of devised generalized non-fragile asynchronous feedback controller are assumed to run asynchronously with neutral Markov jump systems, which is described by a hidden Markov model. The sufficient conditions for the solvability of generalized non-fragile asynchronous feedback control problem are obtained based on decomposed free weighting matrices technique and linear matrix inequalities. The usefulness and effectiveness of output tracking based on generalized non-fragile asynchronous feedback controller are demonstrated by a numerical example and a practical example of neutral partial element equivalent circuit.

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Data availability statement

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

The authors would like to thank the Editors and the Referees for their valuable comments and suggestions, which helped to greatly improve the work. This work was supported by the National Natural Science Foundation of China under Grants 62173174, 61773191, 61973148, 62003154; Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant 2019KJI010; the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant ZR2016JL025; Undergraduate Education Reform Project of higher Education in Shandong Province under Grant M2018X047; Liaocheng University Education Reform Project Foundation under Grants G201811, 26322170267.

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  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong, 252059, People’s Republic of China

    Jie Wang, Guangming Zhuang, Jianwei Xia & Guoliang Chen

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  1. Jie Wang
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Correspondence to Guangming Zhuang.

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Wang, J., Zhuang, G., Xia, J. et al. Generalized non-fragile asynchronous mixed \(H_\infty \) and passive output tracking control for neutral Markov jump systems. Nonlinear Dyn 106, 523–541 (2021). https://doi.org/10.1007/s11071-021-06829-x

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