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Stability and \({L_{\infty }}\)-Gain Analysis for Positive Switched Systems with Time-Varying Delay Under State-Dependent Switching

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Abstract

This paper investigates the problems of stability and \({L_\infty }\)-gain analysis for a class of positive switched systems with time-varying delay. Attention is focused on designing a state-dependent switching rule such that the system satisfies a prescribed \({L_\infty }\)-gain performance level, where the proposed scheme does not require the switching instants to be known in advance. By constructing an appropriate co-positive type Lyapunov–Krasovskii functional, sufficient conditions for exponential stability with \({L_\infty }\)-gain performance of the underlying systems are derived. Furthermore, the stability along the switching surface is analyzed. Finally, two examples are presented to demonstrate 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 under Grant No. KYLX-0371.

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Authors and Affiliations

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

    Shuo Li & Zhengrong Xiang

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  1. Shuo Li
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  2. Zhengrong Xiang
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Correspondence to Zhengrong Xiang.

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Li, S., Xiang, Z. Stability and \({L_{\infty }}\)-Gain Analysis for Positive Switched Systems with Time-Varying Delay Under State-Dependent Switching. Circuits Syst Signal Process 35, 1045–1062 (2016). https://doi.org/10.1007/s00034-015-0099-0

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  • DOI: https://doi.org/10.1007/s00034-015-0099-0

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