By Topic

Almost sure stability of discrete-time switched linear systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Xiongping Dai ; Dept. of Math., Nanjing Univ., Nanjing, China ; Yu Huang ; MingQing Xiao

In this paper, we study the stability of discrete-time switched linear systems via symbolic topology formulation and the multiplicative ergodic theorem. A sufficient and necessary condition for µA-almost sure stability is derived, where µA is the Parry measure of the topological Markov chain with a prescribed transition (0,1)-matrix A. The obtained µA-almost sure stability is invariant under small perturbations of the system. The topological description of stable processes of switched linear systems in terms of Hausdorff dimension is given, and it is shown that our approach captures the maximal set of stable processes for linear switched systems. The obtained results cover the stochastic Markov jump linear systems, where the measure is the natural Markov measure defined by the transition probability matrix. We further show that if the switched system is periodically switching stable, then (i) it is almost sure exponentially stable for any Markov probability measures; (ii) the set of stable switching sequences has the same Hausdorff dimension as the one for the entire set of switching sequences.

Published in:

Control and Automation (ICCA), 2010 8th IEEE International Conference on

Date of Conference:

9-11 June 2010