- A novel characterization of the integral Inputto-
State Stability (iISS) property is introduced for multistable
systems whose dynamics are periodic with respect to a part of
the state. First, the concepts of iISS-Leonov functions and output
smooth dissipativity are introduced, then their equivalence
to the properties of bounded-energy-bounded-state and global
attractiveness of solutions in the absence of disturbances are
proven. The proposed approach permits to relax the usual
requirements of positive definiteness and periodicity of the iISSLyapunov
functions. Moreover, the usefulness of the theoretical
results is illustrated by a robustness analysis of a nonlinear
pendulum with a constant bias input and an unbounded statedependent
input coefficient.