This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations. Readership Graduate students and research mathematicians interested in control theory and nonlinear partial differential equations. Reviews "This well written book by Jean-Michel Coron, one of the world leading experts in the field, enables the reader to enter the difficult subject and to understand the most important methods used here. A book like this was urgently needed." *-- Zentralblatt MATH* "Throughout of the book, the author gives extensive historical comments and he mentions a great number of additional results." *-- Mathematical Reviews* |