Embedding of time-varying contractive systems in lossless realizations (Q1894655)

The lossless embedding problem considers the possibility of extending a given contractive system so that it becomes the partial input-output operator of a lossless system. The problem is solved here for discrete- time time-varying systems with finite state dimensions. The procedure gives rise to a time-varying Riccati equation which is shown to have a closed-form solution. This is an excellent paper that extends the classical time invariant theory to the time varying context. There are many applications of this work, and it is a valuable contribution. However, the paper is not for the mathematically timid.