This paper presents the qualitative heterogeneous control framework, a methodology for the design of a controlled hybrid system based on attractors and transitions between them. This framework designs a robust controller that can accommodate bounded amounts of parametric and structural uncertainty. This framework provides a number of advantages over other similar techniques. The local models used in the design process are qualitative, allowing the use of partial knowledge about system structure, and nonlinear, allowing regions and transitions to be defined in terms of dynamical attractors. In addition, we define boundaries between local models in a natural manner, appealing to intrinsic properties of the system. We demonstrate the use of this framework by designing a novel control algorithm for the cart-pole system. In addition, we illustrate how traditional algorithms, such as linear quadratic regulators, can be incorporated within this framework. The design is validated by experiments with a physical system.