A circle criterion for strong integral input-to-state stability

Christopher Guiver, Hartmut Logemann

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We present sufficient conditions for integral input-to-state stability (iISS) and strong iISS of the zero equilibrium pair of continuous-time forced Lur'e systems, where by strong iISS we mean the conjunction of iISS and small-signal ISS. Our main results are reminiscent of the complex Aizerman conjecture and the well-known circle criterion. We derive a number of corollaries, including a result on stabilisation by static feedback in the presence of input saturation. In particular, we identify classes of forced Lur'e systems with saturating nonlinearities which are strongly iISS, but not ISS.
Original languageEnglish
Article number108641
Early online date24 Oct 2019
Publication statusPublished - 1 Jan 2020


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