Characterization of Integral Input-to-State Stability for Nonlinear Time-Varying Systems of Infinite Dimension

For large classes of infinite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and combination global uniform asymptotic under zero input (0-GUAS) property uniformly bounded-energy input/bounded state is established a reasonable assumption continuity trajectories with respect to at input. By particularizing specific instances such as time-delay or semilinear over Banach spaces, sufficient conditions are given in terms functions defining dynamics. In addition, it also shown that for systems whose nonlinear term satisfies an affine-in-the-state norm bound, holds iISS becomes equivalent just 0-GUAS, fact known hold bilinear systems. An additional important aspect notion considered more general than standard one.