  We consider interconnected nonlinear systems with external inputs, where each
of the subsystems is assumed to be input-to-state stable (ISS). Sufficient
conditions of small gain type are provided guaranteeing that the
interconnection is ISS with respect to the external input. To this end we
extend recently obtained small gain theorems to a more general type of
interconnections. The small gain theorem provided here is applicable to
situations where the ISS conditions are formulated differently for each
subsystem and are either given in the maximization or the summation sense.
Furthermore it is shown that the conditions are compatible in the sense that it
is always possible to transform sum formulations to maximum formulations
without destroying a given small gain condition. An example shows the
advantages of our results in comparison with the known ones.
