Systems Theory: Regional Analysis of Infinite Dimensional Linear Systems

International audienceThe published literature related to distributed parameter systems theory is quite large, and it is not feasible in a single book to give a detailed review on the wide historical development of all of it. Our choice of what to cover was motivated by the following consideration. Since distributed parameter systems evolve in time and space, the research investigations on their analysis and control focus on considering the whole system domain for any study. We feel strongly that within this research field, animportant consideration was missing; that of considering that the system may give raise to prescribed subdomains (regions) where one has to achieve an objective. This is the case of so many applications ranging from engineering to life sciences. For that reason, covering classical prerequisite in analysis and control areas, we have devoted the book to the extension of the classical distributed parameter results to regional ones.Students of mathematics do not come into contacts with distributed parameter systems during their classes. They are introduced to them when they start research and often they are influenced by the knowledge and the advice of experimented scientists. This was our case at the very beginning of these research investigations in the mid 70’s. We would liketo express our special thanks to many of them and mainly late Professor Anthony J. Pritchard (University of Warwick, GB) and late Professor J.L. Lions (College de France) who were so encouraging in front of our determination in driving an academic carrier. We also express our thanks to our co-workers and research students. We wish to acknowledge the feedback from all those who took courses based on various parts of this book.This book may be used by graduate students in mathematics, engineering, physics, and even by students from other fields such as life or environmental sciences. This book may also be used as an information source for researchers and education professionals. We assume that the readers already know the basic concepts of analysis and control of distributedparameter systems