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Stability and \(l_{1}\)-Gain Analysis for Switched Delay Positive Systems with Stable and Unstable Subsystems

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Abstract

In this paper, we investigate the problems of stability and \(l_{1}\)-gain performance analysis for discrete-time switched delay positive systems with stable and unstable subsystems. First, using a class of multiple copositive Lyapunov–Krasovskii function approach, sufficient stability conditions are proposed for the considered system with average dwell time switching. Then, based on the stability results, sufficient conditions that guarantee the system to have \(l_{1}\)-gain performance are developed. All the proposed conditions can be solved by LMI toolbox. Finally, we take an example to verify the effectiveness of the results.

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Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (61203123), the Liaoning Excellent Talents in University (LR2014035), and the Shandong Provincial Natural Science Foundation, China (ZR2012FQ019).

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Authors and Affiliations

  1. College of Information and Control Engineering, China University of Petroleum, Qingdao, 266555, People’s Republic of China

    Ruiqin Shi & Xuemin Tian

  2. College of Engineering, Bohai University, Jinzhou, 121013, People’s Republic of China

    Xudong Zhao & Xiaolong Zheng

Authors
  1. Ruiqin Shi
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  2. Xuemin Tian
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  3. Xudong Zhao
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  4. Xiaolong Zheng
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Correspondence to Xudong Zhao.

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Shi, R., Tian, X., Zhao, X. et al. Stability and \(l_{1}\)-Gain Analysis for Switched Delay Positive Systems with Stable and Unstable Subsystems. Circuits Syst Signal Process 34, 1683–1696 (2015). https://doi.org/10.1007/s00034-014-9910-6

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  • DOI: https://doi.org/10.1007/s00034-014-9910-6

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