Stability of higher-order discrete-time Lur’e systems

E. Sarkans, H. Logemann

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We consider discrete-time Lur’e systems obtained by applying nonlinear feedback to a system of higher-order difference equations (ARMA models). The ARMA model relates the inputs and outputs of the linear system and does not involve any internal or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability, a concept which is very much reminiscent of input-to-state stability.
Original languageEnglish
Pages (from-to)183-211
Number of pages30
JournalLinear Algebra and its Applications
Early online date26 May 2016
Publication statusPublished - 1 Oct 2016


  • Absolute stability, ARMA models, circle criterion, complexified Aizerman conjecture, global asymptotic stability, input-to-output stability, input-output systems, Lur’e systems, polynomial matrices, stability in the large


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