Interpreting the iISS Small-Gain Theorem as Transient Plus ISS Small-Gain Regulation

Hiroshi Ito (1) , Randy Freeman (2) , Antoine Chaillet (3)

1 Kyutech - Kyushu Institute of Technology
2 EECS - Department of Electrical Engineering and Computer Science
3 L2S - Laboratoire des signaux et systèmes

This paper addresses the problem of establishing stability of interconnections of integral input-to-state stable (iISS) systems. Recently, the small-gain theorem for input-tostate stable (ISS) systems has been extended to the class of iISS systems. It has been also proved that at least one of the two iISS subsystems comprising a feedback interconnection needs to be ISS with respect to the state of the other subsystem for guaranteeing the iISS of the overall system. This paper shows that making use of this necessary condition enables to provide more insight on the iISS small gain theorem by giving an alternative proof of this result from the perspective of transient plus ISS small-gain regulation.

Mots clés: ISS; iISS; feedback interconnection

Domaines: Automatique / Robotique

Hiroshi Ito, Randy Freeman, Antoine Chaillet. Interpreting the iISS Small-Gain Theorem as Transient Plus ISS Small-Gain Regulation. 49th IEEE Conference on Decision and Control, Dec 2010, Atlanta, United States. 6 p. ⟨hal-00522198⟩