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A continuous feedback approach to global strong stabilization of nonlinear systems
Abstract
We present a continuous feedback approach to the problem of global strong stabilization, for genuinely nonlinear systems that may not be stabilized, even locally, by any smooth feedback. We describe conditions under which it is possible to prove, while no smooth controllers exist, the existence of continuous state feedback control laws that achieve global strong stability (GSS) in the sense of Kurzweil (1956). The proof is constructive and carried out by developing a machinery, which combines the theory of homogeneous systems with the idea of adding a power integrator, for the explicit construction of globally stabilizing continuous controllers. We then illustrate, by means of examples, how this machinery can be used to overcome the topological obstruction caused by smooth feedback, and hence resulting in new solutions to a variety of open control problems, including global stabilization of an underactuated unstable two degree of freedom mechanical system.
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Cited by
Li, J., Ji, R., Liang, X., Ge, S. S., & Yan, H. (2022) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2022.3218574 · Cited by 659
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Ding, S., Liu, L., & Zheng, W. X. (2017) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2017.2682024 · Cited by 414
A new approach to fast global finite-time stabilization of high-order nonlinear system
Sun, Z.-Y., Yun, M.-M., & Li, T. (2017) · Automatica · doi:10.1016/j.automatica.2017.04.024 · Cited by 292
Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions
Ding, S., Wang, J., & Zheng, W. X. (2015) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2015.2448064 · Cited by 162
Yu, X., & Lin, W. (2022) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2022.3197558 · Cited by 22
Self-citation
Metadata
- Authors
- Qian, C., & Lin, W.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2001-07
- Volume
- 46
- Issue
- 7
- Pages
- 1061-1079
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2167175335
- Cited by
- 1,377
- References
- 0
- FWCI
- 28.70
- Type
- journal article
- Language
- en
- Open access
- closed
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