Integral-Input-to-State Stability of Switched Nonlinear Systems under Slow Switching

In this paper we study integral-input-to-state stability (iISS) of nonlinear switched systems with jumps. We demonstrate by examples that iISS is not always preserved under slow enough dwell time switching, and then we present sufficient conditions for iISS to be preserved under slow switching. These conditions involve, besides a sufficiently large dwell time, some additional properties of comparison functions characterizing iISS of the individual modes. When the sufficient conditions that guarantee iISS are only partially satisfied, we are then able to conclude weaker variants of iISS, also introduced in this work. As an illustration, we show that switched systems with bilinear zero-input-stable modes are always iISS under sufficiently large dwell time.