  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 (Chai and Sanfelice, 2019), 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.
