A Characterization of Integral ISS for Switched and Time-varying Systems
Provides a foundational characterization for iISS in switched and time-varying systems, addressing a gap where converse Lyapunov theorems are unavailable.
The paper characterizes integral input-to-state stability (iISS) for switched and time-varying systems, showing that existing characterizations are insufficient and providing necessary and sufficient conditions.
Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This note provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics.