The set of stable switching sequences for discrete-time linear switched systems Academic Article

abstract

• In this paper we study the characterization of the asymptotical stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence. The obtained result reveals an underlying fundamental principle: a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them, provided that the switching is arbitrary. We also develop frequency and density indexes to identify those asymptotically stable switching sequences of the system. 2010 Elsevier Inc.

authors

• Huang, Tingwen

published proceedings

• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

author list (cited authors)

• Huang, Y. u., Luo, J., Huang, T., & Xiao, M.

citation count

• 12

complete list of authors

• Huang, Yu||Luo, Jun||Huang, Tingwen||Xiao, MingQing

publication date

• May 2011

publisher

• Elsevier  Publisher

published in

• Journal of Mathematical Analysis and Applications  Journal

keywords

• Asymptotically Stability
• Discrete-time Switched Linear Systems
• Ergodic Probability Measure
• Hausdorff Dimension

Digital Object Identifier (DOI)

• 10.1016/j.jmaa.2010.11.053

start page

• 732

end page

• 743

volume

• 377

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jmaa.2010.11.053