  This paper delves into the problem of computing robust controlled invariants
for monotone continuous-time systems, with a specific focus on lower-closed
specifications. We consider the classes of state monotone (SM) and
control-state monotone (CSM) systems, we provide the structural properties of
robust controlled invariants for these classes of systems and show how these
classes significantly impact the computation of invariants. Additionally, we
introduce a notion of feasible points, demonstrating that their existence is
sufficient to characterize robust controlled invariants for the considered
class of systems. The study further investigates the necessity of reducing the
feasibility condition for CSM and Lipschitz systems, unveiling conditions that
guide this reduction. Leveraging these insights, we construct an algorithm for
the computation of robust controlled invariants. To demonstrate the
practicality of our approach, we applied the developed algorithm to the coupled
tank problem.
