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Accurate estimation of the largest divergence rate for a class of the 3rd-order switched linear systems

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Abstract

The largest divergence rate is a characterization of the stability behavior for dynamic systems, which has been proven to be equal to the least possible common matrix set measure (extreme measure) of switched linear systems. To determine the largest divergence rate is an interesting and open problem. In this paper, an algorithm is introduced to estimate the largest divergence rate for a class of the 3rd-order switched linear systems, by which any desired accurate estimation could be derived. It explores a way to determine the largest divergence rate for the 3rd-order switched linear systems. Furthermore, the accurate estimation provides a qualitative and quantitative analysis for guaranteed stability of switched linear systems.

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Authors and Affiliations

  1. College of Automation Science and Engineering, South China University of Technology, Guangzhou Guangdong, 510640, China

    Jiandong Xiong & Zhendong Sun

Authors
  1. Jiandong Xiong
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  2. Zhendong Sun
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Corresponding author

Correspondence to Zhendong Sun.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 60925013, 61273121).

Jiandong XIONG received his B.S. and M.S. degrees from Zhengzhou University in 2005 and 2009, respectively. Currently, he is a Ph.D. candidate at South China University of Technology. His research interests include switched and hybrid systems.

Zhendong SUN was a professor with College of Automation Science and Engineering, South China University of Technology. He is currently a researcher with Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His interests include switched systems and nonlinear control.

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Xiong, J., Sun, Z. Accurate estimation of the largest divergence rate for a class of the 3rd-order switched linear systems. J. Control Theory Appl. 11, 513–516 (2013). https://doi.org/10.1007/s11768-013-2093-z

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  • DOI: https://doi.org/10.1007/s11768-013-2093-z

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