Simple sufficient tests are introduced for almost-sure exponential stability of discrete-time jump parameter systems. These stability criteria are based on the Furstenberg-Kesten theorem. The results are then used in the analysis and design of stabilizing controllers for discrete-time jump parameter systems to achieve reliable performance despite the abrupt changes. A novel almost-sure stabilization algorithm is proposed. It takes advantage of the computationally efficient linear matrix inequality (LMI) framework. A numerical example is given to illustrate the strengths and weaknesses of the introduced design technique.