Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non- Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using H'older continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty.

Main Author: Nersesov, Sergey.
Other Authors: Haddad, Wassim., Hui, Qing.
Language: English
Published: 2007
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:178298
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dc_source_str_mv Proceedings of the 2007 American Control Conference, Marriott Marquis Hotel at Times Square, New York City, USA, July 11-13, 2007, pg. 4812-4816.
author Nersesov, Sergey.
author_s Nersesov, Sergey.
spellingShingle Nersesov, Sergey.
Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
author-letter Nersesov, Sergey.
author_sort_str Nersesov, Sergey.
author2 Haddad, Wassim.
Hui, Qing.
author2Str Haddad, Wassim.
Hui, Qing.
dc_title_str Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
title Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
title_short Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
title_full Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
title_fullStr Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
title_full_unstemmed Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
collection_title_sort_str finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
title_sort finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
description Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non- Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using H'older continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty.
publishDate 2007
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dc.title Finite-time stabilization of nonlinear dynamical systems via control vector lyapunov functions.
dc.creator Nersesov, Sergey.
Haddad, Wassim.
Hui, Qing.
dc.description Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non- Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using H'older continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty.
dc.date 2007
dc.identifier vudl:178298
dc.source Proceedings of the 2007 American Control Conference, Marriott Marquis Hotel at Times Square, New York City, USA, July 11-13, 2007, pg. 4812-4816.
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