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Finite time stabilization of a perturbed double integrator with unilateral constraints

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)

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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: Faculties > Sciences > School of Engineering and Digital Arts > Instrumentation, Control and Embedded Systems
Depositing User: Harshal Oza
Date Deposited: 01 Feb 2014 18:07 UTC
Last Modified: 29 May 2019 11:49 UTC
Resource URI: (The current URI for this page, for reference purposes)
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