Timing contracts for embedded controller implementation specify the constraints on the time instants at which certain operations are performed such as sampling, actuation, computation, etc. In this paper, we consider the problem of verifying the stability of embedded control systems under such timing contracts. Reformulating the problem in the framework of impulsive linear systems, we provide theoretical conditions for stability and a verification algorithm based on reachability analysis. In the second part of the paper, given a model of the plant and of the controller we propose an approach to synthesize timing contracts that guarantee stability.