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Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin

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Title: Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin
Authors: Back, J.1 jh100@snu.ac.kr, Cheong, S.G.2 cheongsg@hotmail.com, Shim, H.2 hshim@snu.ac.kr, Seo, J.H.2 jhseo@snu.ac.kr
Source: Systems & Control Letters. Nov2007, Vol. 56 Issue 11/12, p742-752. 11p.
Subjects: Nonlinear systems, Systems theory, Lyapunov functions, Real numbers
Abstract: Abstract: We present a continuous feedback stabilizer for nonlinear systems in the strict-feedback form, whose chained integrator part has the power of positive odd rational numbers. Since the power is not restricted to be larger than or equal to one, the linearization of the system at the origin may fail. Nevertheless, we show that the closed loop system is globally asymptotically stable (GAS) with the proposed continuous (but, possibly not differentiable) feedback. We formulate a condition that enables our design by characterizing the powers of the given system. The condition also shows that our result is an extension of Qian and Lin [Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems Control Lett. 42 (2001) 185–200] where the power of odd positive integers has been considered. New result on the global finite time stabilization problem is also presented. [Copyright &y& Elsevier]
Copyright of Systems & Control Letters is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Abstract: We present a continuous feedback stabilizer for nonlinear systems in the strict-feedback form, whose chained integrator part has the power of positive odd rational numbers. Since the power is not restricted to be larger than or equal to one, the linearization of the system at the origin may fail. Nevertheless, we show that the closed loop system is globally asymptotically stable (GAS) with the proposed continuous (but, possibly not differentiable) feedback. We formulate a condition that enables our design by characterizing the powers of the given system. The condition also shows that our result is an extension of Qian and Lin [Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems Control Lett. 42 (2001) 185–200] where the power of odd positive integers has been considered. New result on the global finite time stabilization problem is also presented. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Systems & Control Letters is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Systems theory
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      – SubjectFull: Lyapunov functions
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              Text: Nov2007
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