Title: ISS Property with Respect to Boundary Disturbances for a Class of Riesz-Spectral Boundary Control Systems,
Abstract: This paper deals with the establishment of Input-to-State Stability (ISS)
properties for infinite dimensional systems with respect to both boundary and
distributed disturbances. First, an ISS estimate is established with respect to
finite dimensional boundary disturbances for a class of Riesz-spectral boundary
control systems satisfying certain eigenvalue constraints. Second, a concept of
weak solutions is introduced in order to relax the disturbances regularity
assumptions required to ensure the existence of strong solutions. The proposed
concept of weak solutions, that applies to a large class of boundary control
systems which is not limited to the Riesz-spectral ones, provides a natural
extension of the concept of both strong and mild solutions. Assuming that an
ISS estimate holds true for strong solutions, we show the existence, the
uniqueness, and the ISS property of the weak solutions.