SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2546-2569, January 2021.
The paper is devoted to stability analysis of discrete-time time-delay systems, obtained after explicit Euler discretization of (locally) homogeneous continuous-time models. The results are derived by applying the Lyapunov--Krasovskii theory. A generic structure of the functional is given that suits for any homogeneous system of nonzero degree (and it can also be used for any dynamics admitting a homogeneous approximation). The obtained conditions are utilized to demonstrate stability for a discretized delayed locally homogeneous planar system with negative and positive degrees.

中文翻译：

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Lyapunov--离散齐次系统的Krasovskii泛函

SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2546-2569 页，2021
年1 月。该论文致力于离散时间时滞系统的稳定性分析，在（局部）齐次连续时间的显式欧拉离散化后获得楷模。结果是通过应用 Lyapunov--Krasovskii 理论得出的。泛函的通用结构适用于任何非零阶的齐次系统（它也可以用于任何允许齐次近似的动力学）。所获得的条件用于证明具有负度和正度的离散延迟局部齐次平面系统的稳定性。