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Stability and stabilization of block-cascading switched linear systems

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Abstract

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is (QLFs) is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

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Authors and Affiliations

  1. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, PRC

    Ya-Hong Zhu & Dai-Zhang Cheng

Authors
  1. Ya-Hong Zhu
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  2. Dai-Zhang Cheng
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Correspondence to Ya-Hong Zhu.

Additional information

Supported partly by National Natural Science Foundation of PRC (No. 60343001, 60274010, 66221301 and 60334040)

Ya-Hong Zhu received her B.Sc. degree in Department of Mathematics from Soochow University, Suzhou, China in 2002. Since 2002, she has been a postgraduate student in the Institute of Systems Science, Chinese Academy of Sciences.

Her research interests include nonlinear control systems, switched systems.

Dai-Zhan Cheng graduated from Tsinghua University in 1970, received his M.Sc from Graduate School, Chinese Academy of Sciences (CAS) in 1981, Ph.D. from Washington University in 1985. Since 1990, he is a professor with the Institute of Systems Science, Academy of Mathematics and Systems Science (AMSS), CAS.

He is the author/coauthor of 160 journal papers, 6 books and 80 conference papers. His research interests include nonlinear control systems, switched systems, Hamiltonian systems and numerical realization for control design.

Prof. Cheng is currently chairman of Technical Committee on Control Theory, CSA, and IEEE Fellow.

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Zhu, YH., Cheng, DZ. Stability and stabilization of block-cascading switched linear systems. Int J Automat Comput 3, 404–413 (2006). https://doi.org/10.1007/s11633-006-0404-2

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  • DOI: https://doi.org/10.1007/s11633-006-0404-2

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