Homogeneous Differentiator Design using Implicit Lyapunov Function Method

Andrey Polyakov 1 Denis Efimov 1, 2 Wilfrid Perruquetti 1, 2, 3
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : The Implicit Lyapunov Function (ILF) for a class of homogeneous systems is introduced and studied. The analysis of homogeneous differentiator using ILF method is presented. Sufficient stability conditions for homogeneous differentiator are obtained and represented by a parameterized system of Linear Matrix Inequalities (LMI). The differentiation error and convergence time are estimated. The procedure of parameters tuning for homogeneous differentiator is formulated as the semi-definite programming problem with LMI constraints. The obtained theoretical results are supported by numerical simulations.
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Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. Homogeneous Differentiator Design using Implicit Lyapunov Function Method. European Control Conference, IEEE, IFAC, Jun 2014, Strasbourg, France. ⟨hal-01003992⟩

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