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State Feedback \(L_1\)-Gain Control of Positive 2-D Continuous Switched Delayed Systems Via State-Dependent Switching

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Abstract

This paper investigates the stability and \(L_1\)-gain control of two-dimensional (2-D) continuous positive switched delayed systems. Firstly, by constructing an appropriate co-positive Lyapunov–Krasovskii functional, a sufficient condition for asymptotical stability of the system under consideration is derived. Secondly, \(L_1\)-gain performance analysis of the underlying system is investigated. Thirdly, a design methodology for state feedback controller is proposed to ensure that the closed-loop system is asymptotically stable with \(L_1\)-gain performance. Finally, an example is provided to show the effectiveness of the proposed method.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61273120 and the Postgraduate Innovation Project of Jiangsu Province (Grant No. KYLX_378).

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Imran Ghous, Shipei Huang & Zhengrong Xiang

  2. Department of Electrical Engineering, COMSATS Institute of Information Technology, Lahore, 54000, Pakistan

    Imran Ghous

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Correspondence to Zhengrong Xiang.

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Ghous, I., Huang, S. & Xiang, Z. State Feedback \(L_1\)-Gain Control of Positive 2-D Continuous Switched Delayed Systems Via State-Dependent Switching. Circuits Syst Signal Process 35, 2432–2449 (2016). https://doi.org/10.1007/s00034-015-0161-y

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