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Smooth stabilization implies coprime factorization
Abstract
It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems; in particular it is proved that smooth stabilization implies smooth input-to-state stabilization.>
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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
A Lyapunov approach to incremental stability properties
Angeli, D. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/9.989067 · Cited by 760
Robust Adaptive Dynamic Programming and Feedback Stabilization of Nonlinear Systems
Jiang, Y., & Jiang, Z.-P. (2014) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2294968 · Cited by 414
A Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems
Liu, T., & Jiang, Z.-P. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2015.2396645 · Cited by 398
Yang, Y., Feng, G., & Ren, J. (2004) · IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans · doi:10.1109/tsmca.2004.824870 · Cited by 396
Metadata
- Authors
- Sontag, E. D.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1989-04
- Volume
- 34
- Issue
- 4
- Pages
- 435-443
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2017493230
- Cited by
- 2,717
- References
- 0
- FWCI
- 28.16
- Type
- journal article
- Language
- en
- Open access
- closed
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- Sontag, E. D. (1989). Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control. https://doi.org/10.1109/9.28018
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