Abstract | ||
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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. |
Year | DOI | Venue |
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2011 | 10.1109/CDC.2011.6160482 | 2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC) |
Keywords | DocType | ISSN |
switches,rigid body,stability analysis,open loop systems,upper bound,robust control,lyapunov function,trajectory,second order,asymptotic stability | Conference | 0743-1546 |
Citations | PageRank | References |
2 | 0.44 | 7 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
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Harshal B. Oza | 1 | 19 | 5.83 |
Yury Orlov | 2 | 520 | 52.75 |
sarah k spurgeon | 3 | 724 | 71.21 |