In this paper, we investigate the practical h-stability problems of some classes of nonlinear systems as an extension of practical exponential stability. We derive some sufficient conditions that guarantee practical h-stability of perturbed systems using Lyapunov’s theory where a new converse theorem is presented. Finally, numerical examples are introduced to illustrate the applicability of the main results.

中文翻译：

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非线性系统实用h稳定性的逆定理

在本文中，我们研究了某些非线性系统的实际h稳定性问题，作为实际指数稳定性的扩展。我们使用李雅普诺夫理论推导了一些足以保证被摄动系统的实际h稳定性的充分条件，其中提出了新的逆定理。最后，通过算例说明了主要结果的适用性。