Semi-global incremental input-to-state stability of discrete-time Lur'e systems

Gilmore, Max; Guiver, Christopher; Logemann, Hartmut

Abstract

We present sufficient conditions for semi-global incremental input-to-state stability of a class of forced discrete-time Lur'e systems. The results derived are reminiscent of well-known absolute stability criteria such as the small gain theorem and the circle criterion. We derive a natural sufficient condition which guarantees that asymptotically (almost) periodic inputs generate asymptotically (almost) periodic state trajectories. As a corollary, we obtain sufficient conditions for the converging-input converging-state property to hold.

Citation

Gilmore, M., Guiver, C., & Logemann, H. (2020). Semi-global incremental input-to-state stability of discrete-time Lur'e systems. Systems and Control Letters, 136, Article 104593. https://doi.org/10.1016/j.sysconle.2019.104593

• Journal Article Type: Article
• Acceptance Date: Nov 22, 2019
• Online Publication Date: Jan 14, 2020
• Publication Date: 2020-02
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Jan 15, 2021
• Journal: Systems & Control Letters
• Print ISSN: 0167-6911
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 136
• Article Number: 104593
• DOI: https://doi.org/10.1016/j.sysconle.2019.104593
• Keywords: Absolute stability, Almost periodicity, Discrete-time systems, Incremental stability, Lur’e systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2677252