Prescribed-time input-to-state stability of infinite-dimensional systems

We address the notion of prescribed-time input-to-state stability (PTISS) for infinite-dimensional systems (InFDSs). We prove a PTISS Lyapunov theorem, which indicates that if the system admits a PTISS Lyapunov functional (PTISS-LF) then it is PTISS. In addition, we provide a sufficient condition for ensuring the existence of a PTISS-LF for certain InFDSs under the framework of Hilbert spaces. As an example, we verify the PTISS property of parabolic equations with in-domain disturbances and conduct numerical simulations to illustrate the obtained result.