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Uniform Stability of Switched Linear Systems: Extensions of LaSalle's Invariance Principle
Abstract
This paper addresses the uniform stability of switched linear systems, where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set. We provide a collection of results that can be viewed as extensions of LaSalle's Invariance Principle to certain classes of switched linear systems. Using these results one can deduce asymptotic stability using multiple Lyapunov functions whose Lie derivatives are only negative semidefinite. Depending on the regularity assumptions placed on the switching signals, one may be able to conclude just asymptotic stability or (uniform) exponential stability. We show by counter-example that the results obtained are tight.
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Citations
Cited by
Goebel, R., Sanfelice, R. G., & Teel, A. R. (2009) · IEEE Control Systems · doi:10.1109/mcs.2008.931718 · Cited by 1,656
Asynchronously switched control of switched linear systems with average dwell time
Zhang, L., & Gao, H. (2010) · Automatica · doi:10.1016/j.automatica.2010.02.021 · Cited by 787
Zhang, L., Zhuang, S., & Shi, P. (2015) · Automatica · doi:10.1016/j.automatica.2015.02.010 · Cited by 260
Metadata
- Authors
- Hespanha, J.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2004-04
- Volume
- 49
- Issue
- 4
- Pages
- 470-482
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2139656224
- Cited by
- 927
- References
- 0
- FWCI
- 62.09
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hespanha, J. (2004). Uniform Stability of Switched Linear Systems: Extensions of LaSalle's Invariance Principle. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2004.825641
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
