Oza, Harshal B., Orlov, Yury V., Spurgeon, Sarah K. (2014) Finite time stabilization of a perturbed double integrator with unilateral constraints. Mathematics and Computers in Simulation, 95 . pp. 200-212. ISSN 0378-4754. (doi:10.1016/j.matcom.2012.02.011) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:38132)
PDF (Restricted due to publisher policy)
Publisher pdf
Language: English Restricted to Repository staff only |
|
|
|
Official URL: http://dx.doi.org/10.1016/j.matcom.2012.02.011 |
Abstract
A discontinuous second order sliding mode (twisting) controller is utilised in a full state feedback setting for the finite time stabilization of a perturbed double integrator in the presence of both a unilateral constraint and uniformly bounded persisting disturbances. The unilateral constraint involves rigid body inelastic impacts causing jumps in one of the state variables. Firstly, a non-smooth state transformation is employed to transform the unilaterally constrained system into a jump-free system. The transformed system is shown to be a switched homogeneous system with negative homogeneity degree where the solutions are welldefined. Secondly, a non-smooth Lyapunov function is identified to establish uniform asymptotic stability of the transformed system. The global, uniform, finite time stability is then proved by utilising the homogeneity principle of switched systems. The novelty lies in achieving finite time stabilization in the presence of jumps in one of the states without the need to analyze the Lyapunov function at the
jump instants. The proposed results are of theoretical significance as they bridge non-smooth Lyapunov analysis, quasi-homogeneity and finite time stability for a class of impact mechanical systems.
Item Type: | Article |
---|---|
DOI/Identification number: | 10.1016/j.matcom.2012.02.011 |
Uncontrolled keywords: | Impact mechanical systems; Non-smooth Lyapunov functions; Quasi-homogeneity; Switched systems; Finite time stability |
Subjects: | T Technology > TJ Mechanical engineering and machinery > Control engineering |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Engineering and Digital Arts |
Depositing User: | Harshal Oza |
Date Deposited: | 01 Feb 2014 18:07 UTC |
Last Modified: | 17 Aug 2022 10:56 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/38132 (The current URI for this page, for reference purposes) |
- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV
- Depositors only (login required):