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A unified Lyapunov function for finite time stabilization of continuous and variable structure systems with resets

Oza, HB; Orlov, YV; Spurgeon, SK; (2016) A unified Lyapunov function for finite time stabilization of continuous and variable structure systems with resets. In: 2016 IEEE 55th Conference on Decision and Control (CDC). (pp. pp. 2201-2206). IEEE Green open access

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Abstract

A unilaterally constrained perturbed double integrator system is studied in this paper. The aim is to establish uniform finite time stability of the non-linear dynamics in the presence of impacts due to the constraints on the position variable. A non-smooth transformation is utilized to first transform the system into a variable structure system that can be studied within the framework of a conventional discontinuous paradigm. Then, a finite time stable continuous controller is used and stability of the closed-loop dynamics is proven by identifying a new set of Lyapunov functions. The results enable continuous and discontinuous cases to be unified using one parameter that defines the set of Lyapunov functions for each case.

Type: Proceedings paper
Title: A unified Lyapunov function for finite time stabilization of continuous and variable structure systems with resets
Event: IEEE 55th Conference on Decision and Control (CDC)
Location: Las Vegas, Nevada, USA
Dates: 12 December 2016 - 14 December 2016
ISBN-13: 9781509018376
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/CDC.2016.7798590
Publisher version: http://ieeexplore.ieee.org/document/7798590/
Language: English
Additional information: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Keywords: Lyapunov methods, Closed loop systems, Stability analysis, Trajectory, Asymptotic stability, Legged locomotion, Time measurement
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1542120
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