A device is often considered novel if it works in a way qualitatively different from those seen before. Furthermore, a designer relies heavily on this qualitative understanding of device behavior when making substantial changes to a design. Thus an approach to design innovation should capture, at its foundation, an engineer’s ability to identify and reason about a device’s salient features with respect to how it works. At the center of my research is a set of representations for capture these salient features for continuous systems (i.e., interaction topologies), a set of reasoning techniques for constructing and manipulating these representations (e.g, temporal qualitative analysis, temporal constraint propagation, the symbolic algebra system Minima, and the terminological reasoning system Iota) and a set of strategies for constructing designs based on these representations (interaction-based design). These have been developed in the context of designing and analyzing simple feedback control systems.