Multichannel Small-Gain Theorems for Large Scale Networked Systems

We consider large scale interconnected systems where some of the interconnections are characterized by uncertain bounded delays. The delays may for instance be due to a communication network connecting some or all of the subsystems. Using a general formulation of comparison functions we derive a small-gain theorem for local practical stability of such large scale systems. The results build on some generalizations of recent results on the class of monotone aggregation functions and almost inversion of general small-gain operators.