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Continuous uniform finite time stabilization of planar controllable systems

Oza, HB; Orlov, YV; Spurgeon, SK; (2015) Continuous uniform finite time stabilization of planar controllable systems. SIAM Journal on Control and Optimization , 53 (3) pp. 1154-1181. 10.1137/120877155. Green open access

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Abstract

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong C<sup>1</sup> Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers.

Type: Article
Title: Continuous uniform finite time stabilization of planar controllable systems
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/120877155
Publisher version: http://dx.doi.org/ 10.1137/120877155
Language: English
Additional information: Copyright © 2015 Society for Industrial and Applied Mathematics. Published by SIAM under the terms of the Creative Commons 4.0 license (https://creativecommons.org/licenses/by/4.0/)
Keywords: uniform finite time stability, Lyapunov functions, homogeneity
UCL classification: UCL
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/1514552
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