Skip to main content

Research Repository

Advanced Search

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

Guiver, Christopher; Logemann, Hartmut


Hartmut Logemann


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.

Journal Article Type Article
Acceptance Date Aug 16, 2019
Online Publication Date Oct 24, 2019
Publication Date 2020-01
Deposit Date Jul 23, 2020
Publicly Available Date Oct 25, 2020
Journal Automatica
Print ISSN 0005-1098
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 111
Article Number 108641
Keywords Asymptotic stabilisation, Circle criterion, Lur’e systems, Robust control of nonlinear systems, Strong iISS
Public URL


You might also like

Downloadable Citations