A note on input-to-state stability of linear and bilinear infinite-dimensional systems

We propose a construction of Lyapunov functions for linear and bilinear infinite-dimensional integral input-to-state stable systems. In contrast to other constructions available in the literature, we do not impose strong restrictions on the type of the bilinear systems. The coercivity of such Lyapunov functions as well as a possible extension to systems with unbounded input operators are discussed.