The small gain theorem as established in two previous papers has been given in terms of a quite general interconnection of two nonlinear subsystems. This note gives a simplified version and a more straightforward proof for the small gain theorem for a simpler interconnection of two nonlinear subsystems by using a different characterization of the input-to-state stable (ISS) concept. The resulting small gain condition features the familiar contraction mapping inequality for time-invariant systems. Moreover, we have also incorporated some type of model uncertainties into the system description, thus making this special version directly applicable to the global robust stabilization and output regulation problems.
['Zhiyong Chen', 'Jie Huang']
A simplified small gain theorem for time-varying nonlinear systems