A relaxed small-gain theorem for interconnected discrete-time systems

R. Geiselhart, M. Lazar, F.R. Wirth

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)
1 Downloads (Pure)


This paper presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem.
Original languageEnglish
Pages (from-to)812-817
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number3
Publication statusPublished - 2015


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