Many books already exist on the topics of digital control and estimation. The prospective reader of this book might well then ask. "why another book in this area?"
One problem with the existing literature is that it emphasizes the differences between discrete and continuous theory. This dichotomy is largely historical in nature and may not be the best approach from a pedagogical viewpoint. For example, shift operators and Z-transforms, which form the basis of most discrete time analyses, are inappropriate when used with fast sampling and have no continuous time counterpart. Our philosophy, as presented in this book, is that the continuous and discrete cases can, and should, be understood under a common framework. We show that this is facilitated if the shift operator is augmented with alternative forms including one which we call the delta operator. Using the latter operator, it becomes evident that all discrete time theory converges smoothly to the appropriate continuous results as the sampling rate increases. An additional, and somewhat unexpected, bonus arising from the use of the alternative operators is that numerical properties can be substantially improved relative to the more traditional shift operator.
Thus, this book presents continuous and discrete control and estimation theory in a unified fashion, highlighting the interrelationships between the two cases. Our firm belief is that this unified view of discrete and continuous theory is much richer and more informative than when either of the two are studied in isolation.