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) estimates for infinite dimen-sional systems with respect to both boundary and distributed disturbances. First, a new approach isdeveloped for the establishment of ISS estimates for a class of Riesz-spectral boundary control systemssatisfying certain eigenvalue constraints. Second, a concept of weak solutions is introduced in order torelax the disturbances regularity assumptions required to ensure the existence of classical solutions.The proposed concept of weak solutions, that applies to a large class of boundary control systemswhich is not limited to the Riesz-spectral ones, provides a natural extension of the concept of bothclassical and mild solutions. Assuming that an ISS estimate holds true for classical solutions, we showthe existence, the uniqueness, and the ISS property of the weak solutions.