There exist various methods for planning nominal trajectories to guide desired behaviours of non-linear systems, along with constructive methods for computing finite-time invariant sets, termed funnels, about locally-stabilized nominal trajectories. In order to achieve a desired behaviour defined by a set of nominal trajectories and their corresponding funnels, one has to switch from one local control to another at the right instances. This paper presents a general hybrid-control framework which is designed for correct switching between locally stabilizing controllers and can be used in conjunction with various approaches for funnel computation. Our framework prescribes exact connectivity conditions to be satisfied by the different funnels used such that the desired behaviour is achieved globally and in a robust manner. Due to its generality, the framework can be applied to implement a wide class of dynamic behaviours. An example of a periodic behaviour governed by our framework is provided.