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Stability of switched systems with average dwell-time
Abstract
It is shown that switching among stable linear systems results in a stable system provided that switching is "slow-on-the-average". In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.
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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
Perspectives and results on the stability and stabilizability of hybrid systems
Decarlo, R. A., Branicky, M. S., Pettersson, S., & Lennartson, B. (2000) · Proceedings of the IEEE · doi:10.1109/5.871309 · Cited by 1,625
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
Output feedback control of switched nonlinear systems using multiple Lyapunov functions
El-Farra, N. H., Mhaskar, P., & Christofides, P. D. (2005) · Systems & Control Letters · doi:10.1016/j.sysconle.2005.04.005 · Cited by 309
The 2017 IEEE International Conference on Fuzzy Systems
(2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2016.2545826 · Cited by 308
Metadata
- Authors
- Hespanha, J. P., & Morse, A. S.
- Venue
- Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)
- Publisher
- IEEE
- Published
- 2003-01-22
- Volume
- 3
- Pages
- 2655-2660
- ISSN
- 0191-2216 (ISSN-L)
- OpenAlex
- W1900371862
- Cited by
- 2,588
- References
- 0
- FWCI
- 75.04
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Hespanha, J. P., & Morse, A. S. (2003). Stability of switched systems with average dwell-time. Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304). https://doi.org/10.1109/cdc.1999.831330
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