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We consider infinite heterogeneous networks, consisting of input-to-statestable subsystems of possibly infinite dimension. We show that the network isinput-to-state stable, provided that the gain operator satisfies a certainsmall-gain condition. We show that for finite networks of nonlinear systemsthis condition is equivalent to the so-called strong small-gain condition ofthe gain operator (and thus our results extend available results for finitenetworks), and for infinite networks with a linear gain operator theycorrespond to the condition that the spectral radius of the gain operator isless than one. We provide efficient criteria for input-to-state stability ofinfinite networks with linear gains, governed by linear and homogeneous gainoperators, respectively.

Nonlinear small-gain theorems for input-to-state stability of infinite interconnections