We provide a generalized version of the
nonlinear small gain theorem for the case of more than two coupled input-to-state stable systems. For this result the interconnection gains are described
in a nonlinear gain matrix, and the small gain condition requires bounds on the image of this gain matrix. The condition may
be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than 1.
We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an
associated lower-dimensional discrete time dynamical system.
Keywords Interconnected systems - Input-to-state stability - Small gain theorem - Large-scale systems - Monotone maps