Integral input-to-state stability of delay systems based on Lyapunov-Krasovskii functionals with point-wise dissipation rate

Antoine Chaillet (1) , Pierdomenico Pepe (2)

1 L2S - Laboratoire des signaux et systèmes
2 UNIVAQ - University of L'Aquila [Italy]

We show that a Lyapunov-Krasovskii functional whose dissipation rate involves solely the current instantaneous value of the state norm is enough to guarantee integral inputto-state stability (iISS). This result generalizes existing sufficient conditions for iISS, where the dissipation rate involves the whole Lyapunov-Krasovskii functional itself, and simplifies their applicability. Moreover, it provides a more natural bridge with the classical condition for global asymptotic stability of input-free systems. The proof strategy we employ relies on a novel characterization of global asymptotic stability, which may be of interest on its own.

Domaines: Automatique / Robotique

Antoine Chaillet, Pierdomenico Pepe. Integral input-to-state stability of delay systems based on Lyapunov-Krasovskii functionals with point-wise dissipation rate. 57th IEEE Conference on Decision and Control (CDC 2018), Dec 2018, Miami, United States. ⟨10.1109/cdc.2018.8619856⟩. ⟨hal-03114579⟩