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

Christopher Guiver; Hartmut Logemann

doi:10.1016/j.automatica.2019.108641

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

Christopher Guiver, Hartmut Logemann

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Abstract

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 language	English
Article number	108641
Journal	Automatica
Volume	111
Early online date	24 Oct 2019
DOIs	https://doi.org/10.1016/j.automatica.2019.108641
Publication status	Published - 1 Jan 2020

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Aug_2019_guiver_logemann_strong_iiss.PDFAccepted author manuscript, 543 KBLicence: CC BY-NC-ND

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title = "A circle criterion for strong integral input-to-state stability",

abstract = "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.",

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AU - Logemann, Hartmut

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N2 - 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.

AB - 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.

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DO - 10.1016/j.automatica.2019.108641

M3 - Article

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VL - 111

JO - Automatica

JF - Automatica

M1 - 108641

ER -

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

Abstract

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