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Finite time stabilization of perturbed double integrator with jumps in velocity

Oza, Harshal B., Orlov, Yury V., Spurgeon, Sarah K. (2011) Finite time stabilization of perturbed double integrator with jumps in velocity. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference. . pp. 4610-4615. IEEE ISBN 978-1-61284-800-6. (doi:10.1109/CDC.2011.6160482) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1109/CDC.2011.6160482

Abstract

In this paper, finite time stabilization of a perturbed double integrator is considered, incorporating jumps in the velocity at the unstable equilibrium. Rigid body inelastic impacts are considered. A robust control synthesis is presented in the presence of uniformly bounded persistent disturbances. The second order sliding mode (twisting) controller is utilized. Firstly, a non-smooth state transformation is employed to transform the original system into a jump-free system. The transformed system is shown to be a switched homogeneous system with negative homogeneity degree whose solutions are well-defined. Secondly, a non-smooth Lyapunov function is identified to establish uniform asymptotic stability of the transformed system. The global finite time stability then follows from the homogeneity principle of switched systems. Thus, using a single Lyapunov function, the global finite time stability of the origin of the system with velocity jumps is established without having to analyze the Lyapunov function at the jump instants. A finite upper bound on the settling time is also computed.

Item Type: Conference or workshop item (Paper)
DOI/Identification number: 10.1109/CDC.2011.6160482
Subjects: T Technology
Divisions: Faculties > Sciences > School of Engineering and Digital Arts
Faculties > Sciences > School of Engineering and Digital Arts > Instrumentation, Control and Embedded Systems
Depositing User: Tina Thompson
Date Deposited: 30 Oct 2013 16:22 UTC
Last Modified: 29 May 2019 11:12 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/35841 (The current URI for this page, for reference purposes)
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