A. Mironchenko. Lyapunov functions for ISS of infinite-dimensional systems with integrable inputs.

Title: Lyapunov functions for input-to-state stability of infinite-dimensional systems with integrable inputs

Talk at IFAC World Congress in Berlin, 2020

0:10 Setting, main definitions
3:54 Definition of ISS Lyapunov functions
9:42 Coercive L_p-ISS small-gain theorem
11:48 Non-coercive L_p-ISS small-gain theorem

Abstract:
In this paper, we extend the ISS Lyapunov methodology to make it suitable for the analysis of ISS w.r.t. inputs from $L_p$-spaces.
We show that the existence of a so-called $L_p$-ISS Lyapunov function implies $L_p$-ISS of a system.
Also, we show that the existence of a noncoercive $L_p$-ISS Lyapunov function implies $L_p$-ISS of a control system provided the flow map is continuous w.r.t. states and inputs and provided the finite-time reachability sets, corresponding to the input space $L_p$ are bounded.