This established and authoritative text focuses on the design and analysis of nonlinear control systems. The author considers the latest research results and techniques in this updated and extended edition. Topics covered include: • local and global decompositions of control systems; • input-ouput maps and realization theory; • nonlinear feedback for single-input/single-output systems and multi-input/multi-output systems; • applications of state feedback; • output regulation and • global stabilization and disturbance attenuation. Examples are given from mechanical, electrical and aerospace engineering. The approach consists of a rigorous mathematical formulation of control problems and respective methods of solution. The two appendices outline the most important concepts of differential geometry and present some specific data not often found in other standard works. This makes __Nonlinear Control Systems__ suitable as a graduate and undergraduate text and as a source of reference. This book introduces nonlinear control systems at a level suitable for graduate students and researchers. Chapter 1 introduces invariant distributions, a fundamental tool in the analysis of the internal structure of nonlinear systems. It is shown that a nonlinear system locally exhibits decompositions into parts similar to those introduced by Kalman for linear systems. Chapter 2 explains to what extent global decompositions may exist, corresponding to a partition of the whole state space into lower dimensional subsets. Chapter 3 describes various formats in which the input-output map of a nonlinear system may be represented, and provides a short description of the fundamentals of realization theory. Chapter 4 illustrates how a series of relevant design problems can be solved for a single-input single-output nonlinear system. It explains how a system can be transformed into a linear and controllable one, discusses the role of the nonlinear analogue of the notion of "zero", and describes the problem of asymptotic tracking, model matching and disturbance decoupling. Chapter 5 covers similar subjects for those multivariable nonlinear systems which can be rendered noninteractive by means of static state feedback, and Chapters 6 and 7 are devoted to control via dynamic feedback for a broader class of multivariable nonlinear systems. The book was first published in 1985 as Volume 72 in the series Lecture Notes in Control and Information Sciences. The new edition has been thoroughly revised and furnished with examples and exercises at the end of each chapter. The purpose of this book is to present a self-contained description of the fun damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985. Front Matter....Pages i-xv Local Decompositions of Control Systems....Pages 1-76 Global Decompositions of Control Systems....Pages 77-104 Input-Output Maps and Realization Theory....Pages 105-135 Elementary Theory of Nonlinear Feedback for Single-Input Single-Output Systems....Pages 137-217 Elementary Theory of Nonlinear Feedback for Multi-Input Multi-Output Systems....Pages 219-291 Geometric Theory of State Feedback: Tools....Pages 293-338 Geometric Theory of Nonlinear Systems: Applications....Pages 339-386 Tracking and Regulation....Pages 387-425 Global Feedback Design for Single-Input Single-Output Systems....Pages 427-469 Back Matter....Pages 471-549
