On input-to-state-stability and integral input-to-state-stability for parabolic boundary control systems

This work contributes to the recently intensified study of input-to-state stability for infinite-dimensional systems. The focus is laid on the relation between input-to-state stability and integral input-to-state stability for linear systems with a possibly unbounded control operator. The main result is that for parabolic diagonal systems both notions coincide, even in the setting of inputs in L
^∞
, and a simple criterion is derived.