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Fixed-time stabilization control for port-Hamiltonian systems

  • Xinggui Liu
  • Xiaofeng LiaoEmail author
Original Paper

Abstract

In this paper, the locally fixed-time and globally fixed-time stabilization problems for the port-Hamiltonian (PH) systems via the interconnection and damping assignment passivity-based control technique are discussed. The definitions of fixed-time stability region (or region of attraction) and fixed-time stability boundary are given in this paper. From this starting point, the sufficient condition of globally fixed-time attractivity of a prespecified locally fixed-time stability region is obtained. Combining the locally fixed-time stability and the globally fixed-time attractivity of a prespecified locally fixed-time stability region, the globally fixed-time stabilization problem for PH system is effectively solved. Furthermore, the globally fixed-time control scheme independent of locally fixed-time stability region has also been derived by constructing a novel Lyapunov function. A illustrative example shows that the results obtained in this paper work very well in fixed-time control design of PH systems.

Keywords

Fixed-time stability region Port-Hamiltonian systems Fixed-time attractivity Stability boundary at infinity 

Notes

Acknowledgements

This work was supported in part by the National Nature Science Foundation of China (Grant Nos. 61472331, 61772434), in part by the National Key Research and Development Program of China (Grant No. 2016YFB0800601), in part by the Fundamental Research Funds for the Central Universities (Grant No. XDJK2015C078) and in part by the Talents of Science and Technology promote plan, Chongqing Science and Technology Commission. The authors have declared that no conflict of interest exists, and this paper has been approved by all authors for publication.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Electronic and Information EngineeringSouthwest UniversityChongqingPeople’s Republic of China
  2. 2.Department of Applied MathematicsYunnan Agricultural UniversityKunmingPeople’s Republic of China
  3. 3.Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information ProcessingChongqingPeople’s Republic of China
  4. 4.College of Computer ScienceChongqing UniversityChongqingPeople’s Republic of China

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