Revisiting the iISS small-gain theorem through transient plus ISS small-gain regulation

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

1 Department of Systems Design and Informatics
2 EECS - Department of Electrical Engineering and Computer Science
3 L2S - Laboratoire des signaux et systèmes

Recently, the small-gain theorem for input-to-state stable (ISS) systems has been extended to the class of integral input-to-state stable (iISS) systems. Feedback connections of two iISS systems are robustly stable with respect to disturbance if an extended small-gain condition is satisfied. It has been proved that at least one of the two iISS subsystems needs to be ISS for guaranteeing globally asymptotic stability and iISS of the overall system. Making use of this necessary condition for the stability, this paper gives a new interpretation to the iISS small gain theorem as transient plus ISS small-gain regulation. The observation provides useful information for designing and analyzing nonlinear control systems based on the iISS small-gain theorem.

Keywords: Integral input-to-state stability; nonlinear interconnected systems; small gain theorem

Domains: Engineering Sciences [physics]; Automatic

Hiroshi Ito, Randy Freeman, Antoine Chaillet. Revisiting the iISS small-gain theorem through transient plus ISS small-gain regulation. Asian Journal of Control, 2013, 15 (1), pp.11-19. ⟨10.1002/asjc.538⟩. ⟨hal-00780483⟩