A remark on integral input to state stability

Integral input to state stability (IISS) is a notion which generalizes the concept of finite gain with respect to integral norms, in the same manner that input to state stability (ISS) generalizes the idea of finite gain with respect to supremum norms. This paper provides a necessary and sufficient characterization of the IISS property, stated in dissipation terms. It also provides a LaSalle-type invariance principle for ISS.