Almost ISS property for feedback connected systems

Small-gain conditions used in analysis of feedback interconnections are contraction conditions which imply certain stability properties. Such conditions are applied to a finite or infinite interval. In this paper we consider the case, when a small-gain condition is applied to several disjunct intervals and use the density propagation condition in the gaps between these intervals to derive global stability properties for an interconnection. This extends and improves recent results from Stein Shiromoto et al. (2015).