It is difficult to create robust, reusable, and reactive behaviors for robots that can be easily extended and combined. Frameworks such as Behavior Trees are flexible but difficult to characterize, especially when designing reactions and recovery behaviors to consistently converge to a desired goal condition. We propose a framework which we call Robust Logical-Dynamical Systems (RLDS), which combines the advantages of task representations like behavior trees with theoretical guarantees on performance. RLDS can also be constructed automatically from simple sequential task plans and will still achieve robust, reactive behavior in dynamic real-world environments. In this work, we describe both our proposed framework and a case study on a simple household manipulation task, with examples for how specific pieces can be implemented to achieve robust behavior. Finally, we show how in the context of these manipulation tasks, a combination of an RLDS with planning can achieve better results under adversarial conditions.