  Input-to-state stability (ISS) unifies the stability and robustness in one
notion, and serves as a basis for broad areas of nonlinear control theory. In
this contribution, we covered the most fundamental facts in the
infinite-dimensional ISS theory with a stress on Lyapunov methods. We consider
various applications given by different classes of infinite-dimensional
systems. Finally, we discuss a Lyapunov-based small-gain theorem for stability
analysis of an interconnection of two ISS systems.
