Deriving a reasonable mathematical model is fundamental to the analysis, design and control of a dynamic system. The most important factor in model-reduction procedures is approximation error. Sometimes, this reduction error is more important over a certain frequency band than other frequencies, and taking account of this has led to the development of frequency weightings in the model-reduction procedure. This book will describe this technique and outline major applications. Topics covered include: an introduction to model reduction and frequency weighted model reduction problems; mathematical methods used in various model reduction techniques; methods for linear systems; computational techniques; balanced realization based methods for both continuous and discrete systems; stability and passivity.