Abstract

We extend an analog of the Chetaev–Malkin–Massera theorem on stability by the first approximation for differential systems to discrete-time systems in which the linear first approximation system is subjected to linear and nonlinear perturbations. The result is stated in terms of the characteristic exponents and the Lyapunov irregularity coefficient of the linear first approximation system.

中文翻译：

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离散情况下第一近似的稳定性定理的一个版本

摘要

我们将关于稳定性的Chetaev-Malkin-Massera定理的一个模拟由微分系统的一阶近似扩展到离散时间系统，在该离散时间系统中，线性一阶近似系统受到线性和非线性摄动。结果以线性第一近似系统的特征指数和Lyapunov不规则系数表示。