On the Lyapunov Matrix of Linear Delay Difference Equations in Continuous Time

Emanuel Rocha (1) , Sabine Mondié (1) , Michaël Di Loreto (2)

1 CINVESTAV-IPN - Departamento de Control Automático
2 MIS - Ampère, Département Méthodes pour l'Ingénierie des Systèmes

The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the case of single or commensurate delays. An approximation is proposed for the non-commensurate case.

Mots clés: Time-Delay SystemsStability AnalysisLyapunov Methods

Domaines: Energie électrique

Emanuel Rocha, Sabine Mondié, Michaël Di Loreto. On the Lyapunov Matrix of Linear Delay Difference Equations in Continuous Time. IFAC-PapersOnLine, 2017, 50 (1), pp.6507 - 6512. ⟨10.1016/j.ifacol.2017.08.1048⟩. ⟨hal-01624277⟩