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

Guiver, Christopher; Logemann, Hartmut

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.

Citation

Guiver, C., & Logemann, H. (2020). A circle criterion for strong integral input-to-state stability. Automatica, 111, Article 108641. https://doi.org/10.1016/j.automatica.2019.108641

• 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
• DOI: https://doi.org/10.1016/j.automatica.2019.108641
• Keywords: Asymptotic stabilisation, Circle criterion, Lur’e systems, Robust control of nonlinear systems, Strong iISS
• Public URL: http://researchrepository.napier.ac.uk/Output/2677256