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Singular value decomposition-based stochastic admissibility and robust extended dissipativity for delayed hybrid descriptor systems under a unified framework

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Abstract

This paper deals with the issue of stochastic admissibility and robust extended dissipative control for uncertain delayed hybrid descriptor systems (DHDSs) under a unified framework. Belonging to a convex bounded domain, the parameter uncertainties are time-invariant and appear in the state matrix, input matrix and disturbance matrix. Firstly, a stochastic Lyapunov–Krasovskii functional is proposed to reflect the information of time-varying delays and Markovian jump modes, and singular value decomposition technique is utilized to derive novel criteria that ensure the stochastic admissibility and robust extended dissipativity of DHDSs. Then, under a unified framework, the desired robustly stabilizing state feedback controller is realized in terms of linear matrix inequalities. Finally, two examples including a numerical example and an oil catalytic cracking process are applied to corroborate the effectiveness of the derived synthesis scheme.

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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 the important comments and valuable suggestions for improving the paper. This work was supported by National Natural Science Foundation of China under Grants 62173174, 61773191, 61973148; Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant 2019KJI010; Graduate education high-quality curriculum construction project for Shandong Province under Grant SDYKC20185; Natural Science Foundation of Shandong Province for Key Projects under Grant ZR2020KA010.

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Authors and Affiliations

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

    Xin Wang, Guangming Zhuang, Jianwei Xia & Huasheng Zhang

  2. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266520, People’s Republic of China

    Yanqian Wang

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  1. Xin Wang
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  2. Guangming Zhuang
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  3. Jianwei Xia
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Correspondence to Guangming Zhuang.

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Wang, X., Zhuang, G., Xia, J. et al. Singular value decomposition-based stochastic admissibility and robust extended dissipativity for delayed hybrid descriptor systems under a unified framework. Nonlinear Dyn 110, 1663–1681 (2022). https://doi.org/10.1007/s11071-022-07716-9

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