Is a point-wise dissipation rate enough to show ISS for time-delay systems?

Antoine Chaillet (1) , Pierdomenico Pepe (2) , Paolo Mason (1) , Yacine Chitour (3, 1)

1 L2S - Laboratoire des signaux et systèmes
2 UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila
3 Université Paris-Saclay

In this paper, we address the question whether input-to-state stability (ISS) of nonlinear time-delay systems is guaranteed when a Lyapunov-Krasovskii func- tional (LKF) satisfies a dissipation inequality in which the dissipation rate in- volves solely the present value of the state. We do not yet confirm or infirm this conjecture, but rather identify growth restrictions, on the LKF or on the vector field ruling the dynamics, under which it holds true. An example taken from the neuroscience literature illustrates our findings. We also list a series of robustness properties that naturally hold under this point-wise dissipation inequality, and indicate possible research directions to confirm our conjecture.

Keywords: Time delay systems; Input-to-state stability

Domains: Engineering Sciences [physics]; Automatic

Antoine Chaillet, Pierdomenico Pepe, Paolo Mason, Yacine Chitour. Is a point-wise dissipation rate enough to show ISS for time-delay systems?. IFAC 2017 - 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, France. ⟨10.1016/j.ifacol.2017.08.2014⟩. ⟨hal-01493650⟩