Brief paper: A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

Authors:
Zhong-Ping Jiang;Iven M. Y. Mareels;Yuan Wang
Affiliations:
Department of Systems Engineering, Australian National University, Canberra ACT 0200, Australia;Department of Engineering, FEIT, Australian National University, ACT 0200, Australia;Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, U.S.A.
Venue:
Automatica (Journal of IFAC)
Year:
1996

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Abstract

The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.