Brief paper: A degree of flexibility in Lyapunov inequalities for establishing input-to-state stability of interconnected systems

Authors:
Hiroshi Ito
Affiliations:
Department of Systems Innovation and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, 820-8502, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

In this paper, a novel approach to constructing flexible Lyapunov inequalities is developed for establishing Input-to-State Stability (ISS) of interconnection of nonlinear time-varying systems. It aims at a useful tool for using nonlinear small-gain conditions by allowing some flexibility in Lyapunov inequalities each subsystem is to satisfy. In the application of the ISS small-gain ''theorem'', achieving a Lyapunov inequality conforming to a nonlinear small-gain ''condition'' is not a straightforward task. The proposed technique provides us with many Lyapunov inequalities with which a single trade-off condition between subsystems gains can establish the ISS property of the interconnected system. Proofs are based on explicit construction of Lyapunov functions.