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

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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.
Original languageEnglish
Article number104593
JournalSystems & Control Letters
Volume136
Early online date14 Jan 2020
DOIs
Publication statusE-pub ahead of print - 14 Jan 2020

Cite this

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title = "Semi-global incremental input-to-state stability of discrete-time Lur’e systems",
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.",
author = "Max Gilmore and Christopher Guiver and Hartmut Logemann",
year = "2020",
month = "1",
day = "14",
doi = "10.1016/j.sysconle.2019.104593",
language = "English",
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journal = "Systems & Control Letters",
issn = "0167-6911",
publisher = "Elsevier",

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T1 - Semi-global incremental input-to-state stability of discrete-time Lur’e systems

AU - Gilmore, Max

AU - Guiver, Christopher

AU - Logemann, Hartmut

PY - 2020/1/14

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N2 - 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.

AB - 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.

U2 - 10.1016/j.sysconle.2019.104593

DO - 10.1016/j.sysconle.2019.104593

M3 - Article

VL - 136

JO - Systems & Control Letters

JF - Systems & Control Letters

SN - 0167-6911

M1 - 104593

ER -