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Positive \(L_1 \) Observer Design for Positive Switched Systems

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Abstract

This paper investigates the problem of \(L_1\) observer design for positive switched systems. Firstly, a new kind of positive \(L_1\) observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive \(L_1\) observer. Under the condition obtained, the estimated error converges to zero exponentially, and the \(L_1\)-gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61273120.

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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

  2. Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 , Grimstad, Norway

    Hamid Reza Karimi

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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. & Karimi, H.R. Positive \(L_1 \) Observer Design for Positive Switched Systems. Circuits Syst Signal Process 33, 2085–2106 (2014). https://doi.org/10.1007/s00034-013-9737-6

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  • DOI: https://doi.org/10.1007/s00034-013-9737-6

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