This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov functions are allowed to be indefinite. Then, under quite general assumptions, we first present a new converse stability theorem for a large class of time-varying systems which will be used to prove certain stability properties of nonlinear systems with perturbation. Therefore, a new Lyapunov function is presented that guarantees global asymptotic stability under some restrictions on the perturbed system. Furthermore, some illustrative examples are presented.

中文翻译：

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时变非线性系统稳定性的不定导数

本文涉及使用基于李雅普诺夫函数的方法对非线性时变系统进行稳定性分析。经典的李雅普诺夫稳定性定理是在李雅普诺夫函数的时间导数允许不定的意义上进行推广的。然后，在相当一般的假设下，我们首先为一大类时变系统提出了一个新的逆稳定性定理，该定理将用于证明具有扰动的非线性系统的某些稳定性特性。因此，提出了一种新的 Lyapunov 函数，它在扰动系统的某些限制下保证全局渐近稳定性。此外，还提供了一些说明性示例。