Input-to-state stability and integral input-to-state stability of non-autonomous infinite-dimensional systems

In this paper, we provide Lyapunov-based tools to establish input-to-state stability (ISS) and integral input-to-state stability (iISS) for non-autonomous infinite-dimensional systems. We prove that for a class of admissible inputs the existence of an ISS Lyapunov function implies the ISS of a system in Banach spaces. Furthermore, it is shown that uniform global asymptotic stability is equivalent to their integral input-to-state stability for non-autonomous generalised bilinear systems over Banach spaces. The Lyapunov method is provided to be very useful for both linear and nonlinear tools including partial differential equations (PDEs). In addition, we present a method for construction of iISS Lyapunov function in Hilbert spaces. Finally, two examples are given to verify the effectiveness of the proposed scheme.