In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show the usefulness and applicability of the theory of stability with respect to a part of variables are provided. In particular, we show that our approach can be applied to the spring-mass-damper model.

中文翻译：

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时变动力系统稳定性新判据：在弹簧-质量-阻尼器模型中的应用

在本文中，我们研究了非线性时变系统的一部分变量的稳定性问题。基于陈述逆定理的李亚普诺夫技术，我们推导了一些关于扰动系统的部分变量保证指数稳定性和实际指数稳定性的充分条件。此外，还提供了说明性示例，以说明稳定性理论对部分变量的有用性和适用性。特别是，我们表明我们的方法可以应用于弹簧-质量-阻尼器模型。