A relaxed lyapunov condition for input-to-state stability of discrete-time nonlinear systems

Grob, D.; Stursberg, Olaf

doi:10.1109/cdc.2016.7798452

2016 IEEE 55th Conference on Decision and Control (CDC) 2016

DOI: 10.1109/cdc.2016.7798452

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A relaxed lyapunov condition for input-to-state stability of discrete-time nonlinear systems

D. Grob

Olaf Stursberg

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2020

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Determining input‐to‐state and incremental input‐to‐state stability of nonpolynomial systems

Voßwinkel

Röbenack

2020

Intl J Robust & Nonlinear

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In this study, we propose constructive ways to determine input-to-state stability (ISS) as well as incremental ISS (ISS) of nonpolynomial dynamical systems. The developed procedures are based on sums-of-square decomposition. This tool is only applicable to polynomial systems. Thus, a rational recast of the nonpolynomial system description is used. This recast generally leads to an increased system order and additional constraints. These constraints must be respected in the resulting formulations. The proposed approach gives a unique and constructive procedure to determine the ISS and the ISS property, which is normally nontrivial and needs a good understanding of the system's dynamics. The proposed approaches are illustrated on several examples. K E Y W O R D S nonlinear feedback control, input-to-state stability, Lyapunov methods, sum-of-squares programming Abbreviations: ISS, input-to-state stability; ISS, incremental input-to-state stability; SOS, sums-of-squares. [Correction added on 3 December 2020, after first online publication: Rick Voßwinkel was designated as corresponding author.] This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Determining input‐to‐state and incremental input‐to‐state stability of nonpolynomial systems

Voßwinkel

Röbenack

2020

Intl J Robust & Nonlinear

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show abstract

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A relaxed lyapunov condition for input-to-state stability of discrete-time nonlinear systems

Cited by 1 publication

References 16 publications

Determining input‐to‐state and incremental input‐to‐state stability of nonpolynomial systems

Determining input‐to‐state and incremental input‐to‐state stability of nonpolynomial systems

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