Abstract In this study, semi-global practical asymptotic stability of a class of nonlinear cascade systems with upper triangular configuration has been investigated. In particular, using general results presented on stabilization of the discrete-time systems, a semi-global practical asymptotic stabilizing controller has been designed and the essential conditions for the semi-global asymptotic stability of this class of nonlinear cascade systems have been presented. The controller-design framework is based on the approximate discrete-time model of the system and the corresponding cross term constructed Lyapunov function. To illustrate the effectiveness of the proposed scheme, it has been applied to some examples and also been compared with other counterpart results in this context.

中文翻译：

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使用交叉项构造的 Lyapunov 泛函稳定离散时间上三角非线性级联系统

摘要 本研究研究了一类具有上三角构型的非线性级联系统的半全局实用渐近稳定性。特别是，利用离散时间系统镇定的一般结果，设计了半全局实用渐近稳定控制器，并给出了这类非线性级联系统半全局渐近稳定的必要条件。控制器设计框架基于系统的近似离散时间模型和相应的交叉项构造的李雅普诺夫函数。为了说明所提出方案的有效性，已将其应用于一些示例，并在此背景下与其他对应结果进行了比较。