A variation of the small gain theorem

The small gain theorem as established in [Z.P. Jiang and I. Mareels, 1997] and [Z.P. Jiang et al., 1994] has been given in terms of a quite general inter-connection of two nonlinear subsystems. This paper gives a more clear-cut version and a more straightforward proof for the small gain theorem for a simpler inter-connection of two nonlinear subsystems by using a different characterization of the ISS concept. 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.