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Stabilization and Finite Time Stabilization of Nonlinear Differential Inclusions Based on Control Lyapunov Function

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Abstract

This paper deals with the stabilization and finite time stabilization of a class of nonlinear differential inclusions (NDI). First, we present the definitions of control Lyapunov function, exponentially stable control Lyapunov function (CLF) and finite time stable CLF for NDI. Then, we design controllers to make the systems asymptotically stable, exponentially stable, and finite time stable, respectively. Finally, an example of discontinuous system is given to show the effectiveness of the designed controllers.

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Acknowledgments

The authors are grateful for Natural Science Foundation of Jiangsu Province of China (BK20130322, BK20130331), Natural Science Fund for Colleges and Universities in Jiangsu Province (13KJB510032), China Postdoctoral Science Foundation (2013M530268, 2013M531401), the Jiangsu Planned Projects for Postdoctoral Research Funds (1202043C, 1301150C), and the Key Technology Research and Development Program of Suzhou, China (SG201319).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Soochow University, Suzhou , 215021, Jiangsu, China

    Jun Huang & Lei Yu

  2. Department of Electrical and Electronics Engineering, Dalian University of Technology, Dalian , 116024, China

    Shangwen Xia

Authors
  1. Jun Huang
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  2. Lei Yu
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  3. Shangwen Xia
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Correspondence to Jun Huang.

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Huang, J., Yu, L. & Xia, S. Stabilization and Finite Time Stabilization of Nonlinear Differential Inclusions Based on Control Lyapunov Function. Circuits Syst Signal Process 33, 2319–2331 (2014). https://doi.org/10.1007/s00034-014-9741-5

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  • DOI: https://doi.org/10.1007/s00034-014-9741-5

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