A small-gain condition for iISS of interconnected retarded systems based on Lyapunov-Krasovskii functionals

Authors:
Hiroshi Ito;Pierdomenico Pepe;Zhong-Ping Jiang
Affiliations:
Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, 820-8502, Japan;Department of Electrical and Information Engineering, University of L'Aquila, 67040 Poggio di Roio, L'Aquila, Italy;Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, NY 11201, USA
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

This paper considers interconnected retarded nonlinear systems. Integral input-to-state stable subsystems and the construction of Lyapunov-Krasovskii functionals for their interconnections are focused on. Both discrete and distributed time-delays in the subsystems and the communication channels are covered. This paper provides a sufficient small-gain type condition for the stability of the interconnected systems with respect to external inputs in the framework of Lyapunov-Krasovskii functionals. Global asymptotic stability is addressed as a special case which deals with time-varying delays in communication channels effectively.