Three model reduction methods are described. These are the discrete balanced realizations of Mullis and Roberts [1],[2] where a characterization of the reduction error is given and a previously unknown L4048931 norm bound on the reduction error, is obtained. Another method is a new model reduction technique for discrete time systems which has the advantage that the reduced order model is balanced and has an L4048931 norm bound on the reduction error. The last method derived is a frequency weighting technique for continuous and discrete systems where it is possible to specify the approximation accuracy with frequency and also, for this method, an L4048931 norm on the weighted reduction error is obtained.