## 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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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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DOI: https://doi.org/10.1007/s00034-015-0161-y

### Keywords

- Positive systems
- 2-D systems
- Switched systems
- State feedback control
- \(L_1\)-gain performance
- Time-varying delay