Proceedings Article10.23919/ACC.2004.1386714
Finite-time stabilization in the large for uncertain nonlinear systems
TL;DR: In this paper, the authors considered the problem of finite-time stabilization for nonlinear systems and proposed a non-Lipschitz continuous, global finite time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function.
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Abstract: We consider the problem of finite-time stabilization for nonlinear systems. In the previous work, it was proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system could be achieved by non-Lipschitz continuous state feedback. The proof was based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method proposed in, for the control of nonlinear systems that are impossible to be dealt with by any smooth feedback. A simpler design algorithm is given for the construction of a non-Lipschitz continuous, global finite-time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function that guarantees finite-time stability.
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Citations
Adaptive finite time stabilization for a class of nonlinear systems
Yiguang Hong,Jiankui Wang,Daizhan Cheng +2 more
- 01 Jan 2004
TL;DR: To solve the global finite time stabilization problem for a class of nonlinear control systems with parametric uncertainties, a constructive control design approach is proposed, and a finite time control law is constructed in the form of continuous time-invariant feedback.
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Output Tracking Problem of Uncertain Nonlinear Systems with High-Order Nonlinearities
Keylan Alimhan,Naohisa Otsuka,Maksat Kalimoldayev,Abilmajin A. Adamov +3 more
- 01 Nov 2015
TL;DR: A continuous state feedback controller is successfully constructed to guarantee the tracking error achieve arbitrarily small in a class of high-order non-linear systems with more general uncertainties.
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Robust finite time controller design for second order nonlinear underactuated mechanical systems
TL;DR: In this paper, a robust finite time control strategy is developed for a class of second order underactuated mechanical systems, which is to drive the tracking error to be zero at the fixed final time.
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Finite-time stabilization of nonsmoothly stabilizable systems
TL;DR: Using the finite-time Lyapunov stability theorem and the nonsmooth feedback design method developed recently, with a suitable twist, it was shown in this article that it is possible to achieve global finite time stabilizability for a significant class of nonlinear systems which has been known not to be smoothly stabilizable, even locally, but can be globally asymptotically stabilized by Holder continuous state feedback.
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Continuous finite-time stabilization of the translational and rotational double integrators
TL;DR: A class of bounded continuous time-invariant finite-time stabilizing feedback laws is given for the double integrator because Lyapunov theory is used to prove finite- time convergence.
A continuous feedback approach to global strong stabilization of nonlinear systems
Chunjiang Qian,Wei Lin +1 more
TL;DR: Conditions under which it is possible to prove the existence of continuous state feedback control laws that achieve global strong stability (GSS) in the sense of Kurzweil (1956) are described.
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Global finite-time stabilization of a class of uncertain nonlinear systems
Xianqing Huang,Wei Lin,Bo Yang +2 more
TL;DR: It is proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Holder continuous state feedback.
1.2K