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Output Strictly Passive \({{\varvec{H}}_\infty }\) Control of Discrete-Time Linear Switched Singular Systems Via Proportional Plus Derivative State Feedback

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Abstract

This work aims to study the problem of output strictly passive \(H_\infty \) control for discrete-time linear switched singular systems. By using multiple storage functions and iteration technique, some sufficient conditions are obtained based on output strict passivity and proportional plus derivative state feedback, which can guarantee that the closed-loop systems are normal and stable and satisfy a given \(H_\infty \) performance. Proportional plus derivative state feedback sub-controllers with explicit expressions are designed. Proportional plus derivative state feedback can not only eliminate impulse phenomena, but also eliminate state jumps caused by incompatible initial conditions of subsystems at switching instants. A numerical example is given to verify the applicability of the results.

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Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, China

    Zairui Gao, Ziyun Wang & Zhicheng Ji

  2. College of Information and Control Engineering, Weifang University, Weifang, China

    Zairui Gao & Yunlong Liu

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  1. Zairui Gao
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  2. Ziyun Wang
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  4. Yunlong Liu
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Correspondence to Zairui Gao.

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This work was supported in part by the National Natural Science Foundation of China under Grants (61802150, 61572237), Shandong Provincial Natural Science Foundation under Grants (ZR2017QF011, ZR2019MF059), Natural Science Foundation of Jiangsu Province under Grant BK20170196, and Doctoral Foundation of Weifang University under Grant 2014BS11.

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Gao, Z., Wang, Z., Ji, Z. et al. Output Strictly Passive \({{\varvec{H}}_\infty }\) Control of Discrete-Time Linear Switched Singular Systems Via Proportional Plus Derivative State Feedback. Circuits Syst Signal Process 39, 3907–3924 (2020). https://doi.org/10.1007/s00034-020-01353-6

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  • DOI: https://doi.org/10.1007/s00034-020-01353-6

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