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Robust Exponential Stabilization for Sampled-Data Systems with Variable Sampling and Packet Dropouts

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Abstract

This paper investigates the problem of robust exponential stabilization for sampled-data systems with variable sampling and packet dropouts. It is assumed that the system parameter uncertainties are norm-bounded and appear in both the state and input matrices. An input delay approach is adopted to model the sample-and-hold behavior with a time-varying delayed control input, and a switched system approach is proposed to model the data-missing phenomenon. On this basis, the sampled-data control system with variable sampling and packet dropouts is modeled as a switched system with time-varying delay. The objective is to design a sampled-data controller to guarantee the robust exponential stability of the resulting closed-loop system. Based on a new piecewise time-dependent Lyapunov functional, novel sufficient conditions are derived for the existence of robustly exponentially stabilizing sampled-data controllers. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are given to demonstrate the effectiveness of the proposed method.

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Acknowledgments

The authors are grateful to the Editor-in-Chief, the Associate Editor, and anonymous reviewers for their constructive comments based on which the presentation of this paper has been greatly improved.

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Authors and Affiliations

  1. Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, 150001, China

    Meng Wang, Mao Wang, Jianbin Qiu & Ligang Wu

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  1. Meng Wang
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  2. Mao Wang
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  3. Jianbin Qiu
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  4. Ligang Wu
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Correspondence to Jianbin Qiu.

Additional information

This work was supported by the National Natural Science Foundation of China (61374031, 61522306, and 61525303), the Self-Planned Task (No. SKLRS201402C) of State Key Laboratory of Robotics and Systems (HIT), the Harbin Special Funds for Technological Innovation Research (2014RFQXJ067), and the Alexander von Humboldt Foundation of Germany.

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Wang, M., Wang, M., Qiu, J. et al. Robust Exponential Stabilization for Sampled-Data Systems with Variable Sampling and Packet Dropouts. Circuits Syst Signal Process 35, 3482–3505 (2016). https://doi.org/10.1007/s00034-015-0212-4

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  • DOI: https://doi.org/10.1007/s00034-015-0212-4

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