We consider the controller synthesis problem for a class of uncertain hybrid dynamical systems. The goal is for the closed loop system to exhibit desired behavior under dynamic uncertainty and exteriors disturbances. The main question is whether there exists a controller such that the closed loop system satisfies the specification. The notion of attainability is introduced to refer to the specified behavior that can be forced to the plant by a control mechanism. We give a method for attainability checking by employing the predecessor operator and backward reachability analysis, and a procedure for controller design by using finite automata and linear programming techniques.