Robust control theory in Hilbert space / Avraham Feintuch

The problem of robust control has been an important subject over the last decades. There exists several techniques for solving this problem all with their own advantages. The state-space techniques gives nice Riccati equations which, for finite-dimensional systems, can be easily computed; the frequency-domain technique can be used for finite- and infinite-dimensional linear, time-invariant systems; and the operator-based technique can solve the problem for time-varying systems. In the present book, the author solves the robust control problem using the operator-based technique. Since this is the technique which can handle the most general class of systems, it is not surprising that the author has to state a lot of preliminary results. This is done in Chapter 2 till 4, with Chapter 4 containing important results concerning factorization. Although these theorems are very technical, the proofs of the results are easy to understand. In Chapter 5, the concept of a linear system is defined as being a linear operator on an extended Hilbert space. In Chapter 6 the concept of stabilization is studied. The approach here is an operator technique version of the coprime factorization of transfer functions. The general problem of model matching is solved in Chapter 7. Robust control problems are studied in Chapter 8 (general case) and in Chapter 10 (gap metric). In the final chapter, the orthogonal embedding problem is solved; the problem means: Given a passive system does there exist a lossless system such that its compression equal the original system? Every chapter ends with some exercises. (Zentralblatt)