This Ph.D. thesis considers the development of new analysis and control techniques for special classes of hybrid systems and discrete event systems. Two particular classes of hybrid systems (piecewise affine systems and max-min-plus-scaling systems), and two particular classes of discrete event systems (max-plus-linear systems and switching max-plus-linear systems) are studied. Using the optimal control framework, model predictive control schemes are designed that make use of the special structure of these systems and that incorporate conditions to guarantee a priori closed-loop asymptotic stability. Stability is obtained by deriving bounds on the tuning parameters or by imposing a terminal set constraint and using an appropriate terminal cost. The thesis considers three main topics: * Optimal control and model predictive control for max-plus-linear systems; * Min-max model predictive control for max-min-plus-scaling systems; * Model predictive control for piecewise affine systems.