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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Xiongping Dai Yu Huang MingQing Xiao |
| Copyright Year | 2010 |
| Description | Author affiliation: Department of Mathematics, Zhongshan( Sun Yat-Sen) University, Guangzhou 510275, China (Yu Huang) || Department of Mathematics, Southern Illinois University, Carbondale, 62901, USA (MingQing Xiao) || Department of Mathematics, Nanjing University, 210093, China (Xiongping Dai) |
| Abstract | 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. |
| Starting Page | 2098 |
| Ending Page | 2103 |
| File Size | 766566 |
| Page Count | 6 |
| File Format | |
| ISBN | 9781424451951 |
| ISSN | 19483457 |
| DOI | 10.1109/ICCA.2010.5524305 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2010-06-09 |
| Publisher Place | China |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Linear systems Switched systems Lyapunov method Mathematics Stability analysis Stochastic systems Hydrogen Switches Automatic control Control systems Hausdorff dimension Discrete-time switched linear system topological Markov chain almost sure stability periodical switching stability Lyapunov exponent |
| Content Type | Text |
| Resource Type | Article |
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