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Finite-time Attractive Ellipsoid Method: Implicit Lyapunov Function Approach

Manuel Mera 1 Andrey Polyakov 2, 1 Wilfrid Perruquetti 1, 2, 3
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : A finite-time version, based on Implicit Lyapunov Functions (ILF), for the Attractive Ellipsoid Method (AEM) is developed. Based on this, a robust control scheme is presented to ensure finite-time convergence of the solutions of a chain of integrators with bounded output perturbations to a minimal ellipsoidal set. The control parameters are obtained by solving a minimization problem of the " size " of the ellipsoid subject to a set of Linear Matrix Inequalities (LMI's) constraints, and by applying the implicit function theorem. A numerical example is presented to support the implementability of these theoretical results.
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https://hal.inria.fr/hal-01227455
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Submitted on : Wednesday, November 11, 2015 - 12:55:49 AM
Last modification on : Tuesday, September 29, 2020 - 12:24:10 PM
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Manuel Mera, Andrey Polyakov, Wilfrid Perruquetti. Finite-time Attractive Ellipsoid Method: Implicit Lyapunov Function Approach. International Journal of Control, Taylor & Francis, 2015, ⟨10.1080/00207179.2015.1118660⟩. ⟨hal-01227455⟩

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