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

Max Gilmore; Christopher Guiver; Hartmut Logemann

doi:10.1016/j.sysconle.2019.104593

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

Max Gilmore, Christopher Guiver, Hartmut Logemann

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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 language	English
Article number	104593
Journal	Systems & Control Letters
Volume	136
Early online date	14 Jan 2020
DOIs	https://doi.org/10.1016/j.sysconle.2019.104593
Publication status	Published - 29 Feb 2020

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10.1016/j.sysconle.2019.104593

gilmore_et_al_semi_global_stability_dt_lureAccepted author manuscript, 407 KBLicence: CC BY-NC-ND

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title = "Semi-global incremental input-to-state stability of discrete-time Lur{\textquoteright}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.",

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AU - Guiver, Christopher

AU - Logemann, Hartmut

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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.

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DO - 10.1016/j.sysconle.2019.104593

M3 - Article

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VL - 136

JO - Systems & Control Letters

JF - Systems & Control Letters

M1 - 104593

ER -

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

Abstract

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