A Bridge between Lyapunov-Krasovskii and Spectral Approaches for Stability of Difference Equations

Sérine Damak (1) , Ali Ferhi (1) , Vincent Andrieu (2) , Michaël Di Loreto (1) , Warody Lombardi (1)

1 AMPERE - Ampère
2 LAGEP - Laboratoire d'automatique et de génie des procédés

In this paper, we analyze the stability properties of a class of systems governed by linear difference equations. Lyapunov stability and asymptotic stability are analyzed using two different approaches, namely Lyapunov-Krasovskii techniques and spectral techniques. In the case of commensurable delays, we carry out an analytical form of the solution, allowing us to determine necessary and sufficient conditions for stability. A link with discrete-time systems is made, and some comments on time-varying delays are proposed.

Domaines: Automatique / Robotique

Sérine Damak, Ali Ferhi, Vincent Andrieu, Michaël Di Loreto, Warody Lombardi. A Bridge between Lyapunov-Krasovskii and Spectral Approaches for Stability of Difference Equations. 11th IFAC Workshop on Time-Delay Systems, Feb 2013, Grenoble, France. pp.30-35, ⟨10.3182/20130204-3-FR-4031.00166⟩. ⟨hal-00957324⟩