Applied and Computational Mathematics

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The Average Dwell Time Condition Is Necessary & Sufficient for Arbitrary Switching Stability of Switched Nonlinear Systems

Received: 12 October 2016    Accepted: 14 November 2016    Published: 08 December 2016
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Abstract

Constrained switching of switched nonlinear systems consists of many classes of switching signals with markedly different features. One of the most important ones is the average dwell time (ADT) switching. For switched systems, it is a well-known result that a switched nonlinear system is globally uniformly asymptotically stable under arbitrary switching sequence if the ADT satisfies the lower bound defined by a real constant value (). In this note, it will be shown that this ADT condition is also necessary.

DOI 10.11648/j.acm.20160506.11
Published in Applied and Computational Mathematics (Volume 5, Issue 6, December 2016)
Page(s) 230-233
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Switched Nonlinear Systems, Multiple Lyapunov Functions, Average Dwell Time, Arbitrary Switching Stability

References
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[11] L. Zhang, H. Gao. Asynchronously switched control of switched linear systems with average dwell time, Automatica, 46: 953-958, 2010.
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Author Information
  • Jiangsu Province Key Laboratory of Aerospace Power Systems, College of Energy & Power Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing, P. R. China

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    Jiqiang Wang. (2016). The Average Dwell Time Condition Is Necessary & Sufficient for Arbitrary Switching Stability of Switched Nonlinear Systems. Applied and Computational Mathematics, 5(6), 230-233. https://doi.org/10.11648/j.acm.20160506.11

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    ACS Style

    Jiqiang Wang. The Average Dwell Time Condition Is Necessary & Sufficient for Arbitrary Switching Stability of Switched Nonlinear Systems. Appl. Comput. Math. 2016, 5(6), 230-233. doi: 10.11648/j.acm.20160506.11

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    AMA Style

    Jiqiang Wang. The Average Dwell Time Condition Is Necessary & Sufficient for Arbitrary Switching Stability of Switched Nonlinear Systems. Appl Comput Math. 2016;5(6):230-233. doi: 10.11648/j.acm.20160506.11

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  • @article{10.11648/j.acm.20160506.11,
      author = {Jiqiang Wang},
      title = {The Average Dwell Time Condition  Is Necessary & Sufficient for Arbitrary Switching Stability of Switched Nonlinear Systems},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {6},
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      doi = {10.11648/j.acm.20160506.11},
      url = {https://doi.org/10.11648/j.acm.20160506.11},
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      abstract = {Constrained switching of switched nonlinear systems consists of many classes of switching signals with markedly different features. One of the most important ones is the average dwell time (ADT) switching. For switched systems, it is a well-known result that a switched nonlinear system is globally uniformly asymptotically stable under arbitrary switching sequence if the ADT satisfies the lower bound defined by a real constant value (). In this note, it will be shown that this ADT condition is also necessary.},
     year = {2016}
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