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. 查看全文>>