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

In this paper, we extend the ISS Lyapunov methodology to make it suitable for the analysis of ISS w.r.t. inputs from Lp-spaces. We show that the existence of a so-called Lp-ISS Lyapunov function implies Lp-ISS of a system. Also, we show that existence of a noncoercive Lp-ISS Lyapunov function implies Lp-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 Lp are bounded.