Global and Local Weighted Homogeneity for Time-Delay Systems

Denis Efimov (1) , Wilfrid Perruquetti (1, 2, 3) , Jean-Pierre Richard (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

The notion of weighted homogeneity is extended to the time-delay systems. It is shown that the stability/instability of homogeneous functional systems on a sphere implies the global stability/instability of the system. The notion of local homogeneity is introduced, a relation between stability/instability of the locally approximating dynamics and the original time-delay system is established using Lyapunov-Razumikhin approach. An implication between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given.

Domaines: Automatique / Robotique

Denis Efimov, Wilfrid Perruquetti, Jean-Pierre Richard. Global and Local Weighted Homogeneity for Time-Delay Systems. Karafyllis I.; Malisoff M.; Mazenc F.; Pepe P. Recent Results on Nonlinear Delay Control Systems, 4, Springer, pp.163--181, 2015, 978-3-319-18071-7. ⟨hal-01185726⟩