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
2 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
3 Centrale Lille

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.

Domaines: Automatique

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⟩