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
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 Centrale Lille

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.

Mots clés: LMI linear matrix inequality; Robust Control; Lyapunov Methods

Domaines: Optimisation et contrôle [math.OC]

Manuel Mera, Andrey Polyakov, Wilfrid Perruquetti. Finite-time Attractive Ellipsoid Method: Implicit Lyapunov Function Approach. International Journal of Control, 2015, ⟨10.1080/00207179.2015.1118660⟩. ⟨hal-01227455⟩