Fitting characterizations of integral ISS notions for multistable state periodic systems

Novel characterizations of the integral Input-to-State Stability (iISS) property are provided for multistable systems with periodic dynamics in a part of the state. The concepts of iISS-Leonov functions and output smooth dissipativity are introduced, and their equivalence to the properties of bounded-energy-bounded-state and global attractiveness of unperturbed solutions are proven. Furthermore, the strong iISS property is examined in terms of the presented iISS-Leonov functions. The proposed approach represents a relaxed characterization of the iISS property for the considered class of systems, in contrast to conventional results, since iISS-Leonov functions are not necessarily positive definite. Finally, the usefulness of the theoretical results is illustrated by a robustness analysis of a synchronous generator with saturated control input.