The input and output normal representations of stable systems are generalized for unstable systems. These are then used to reduce the order of unstable discrete-time linear multivariable systems resulting in reduced order models with the same number of unstable poles as the full order model and with an a priori upper bound on the reduction error. The generalized normal representations are then modified to include a frequency weighting resulting in frequency weighted generalized normal representations. These are used to derive frequency weighted reduced order models for unstable discrete systems with the same number of unstable poles as the full order model and with an a priori upper bound on the frequency weighted reduction error.