systems are considered, another important subject that depends very much on the state-space formulation is perhaps real- time filtering, prediction, and smoothing via the Kalman filter. This subject is treated in our monograph entitled "Kalman Filtering with Real-Time Applications" published in this Springer Series in Information Sciences (Volume 17). For time-invariant systems, the recent frequency domain approaches using the techniques of Adamjan, Arov, and Krein (also known as AAK), balanced realization, and oo H theory via Nevanlinna-Pick interpolation seem very promising, and this will be studied in our forthcoming monograph entitled "Mathematical Ap­ proach to Signal Processing and System Theory". The present elementary treatise on linear system theory should provide enough engineering and mathe­ of these two subjects.