Construction of iISS Lyapunov functions for interconnected parabolic systems

This paper develops tools to construct Lyapunov functions establishing integral input-to-state stability (iISS) and input-to-state stability (ISS) for several classes of nonlinear parabolic equations. Using these constructions and an infinite-dimensional iISS small-gain theorem we provide a stability criterion for interconnections of iISS parabolic systems. We show that for interconnections of partial differential equations it is essential to choose right state and input spaces, especially for iISS subsystems which are not ISS.