Isidori A. Nonlinear Control Systems: An Introduction

Springer, 1985. — 303 p.
This volume was planned as a textbook for a graduate course on nonlinear multivariable feedback systems. Most of it was prepared while the author was teaching a similar course at the Department of Systems Sciences and Mathematics of the Washington University in St. Louis, in the 1983 fall semester. The purpose of the volume is to present a self-contained description of the fundamentals of the theory of nonlinear feedback control systems, with special emphasis on the differential-geometric approach.
In the last decade, differential geometry has proven to be as successful to the study of nonlinear systems as Laplace transform and complex functions theory were in the '50s to the study of single-input single-output linear systems and linear algebra in the '60s to the study of multivariable linear systems. Typical "synthesis" problems like disturbance isolation, noninteraction, shaping of the input-output response via feedback, can be dealt with relative ease, with tools that are well within the reach of a (mathematically oriented) control engineer. The purpose of this volume is to make the reader aquainted with major methods and results, and to make him able to explore the constantly growing literature.