This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a control law if every solution to the closed-loop system that starts from the set stays within the set for all future time, regardless of the value of the disturbances. Building on the first part of this article, which focuses on analysis, in this article, sufficient conditions for generic sets to enjoy such a property are proposed. To construct invariance inducing state-feedback laws, the notion of robust control Lyapunov function for forward invariance is defined. The proposed synthesis results rely on set-valued maps that include all admissible control inputs that keep closed-loop solutions within the set of interest. Results guaranteeing the existence of such state-feedback laws are also presented. Moreover, conditions for the design of continuous state-feedback laws with minimum point-wise norm are provided. Major results are illustrated throughout this article in a constrained bouncing ball system and a robotic manipulator application.

中文翻译：

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混合动力系统集合的前向不变性（第二部分）


本文介绍了用于设计控制律的工具，该控制律可诱导建模为混合包含体的混合动力系统集的鲁棒受控正向不变性。如果从集合开始的闭环系统的每个解在所有未来时间都保持在集合内，则无论扰动的值如何，集合都通过控制律具有鲁棒的受控前向不变性。在本文第一部分重点分析的基础上，本文提出了泛型集享有这种性质的充分条件。为了构造状态反馈定律的不变性，定义了前向不变性的鲁棒控制李亚普诺夫函数的概念。所提出的综合结果依赖于集值映射，其中包括所有允许的控制输入，这些控制输入将闭环解决方案保持在感兴趣的集合内。还提出了保证此类状态反馈定律存在的结果。此外，还提供了设计具有最小逐点范数的连续状态反馈律的条件。本文在约束弹跳球系统和机器人操纵器应用中说明了主要结果。