This is one of the first books presenting stabilizability of nonlinear systems in a well-organized and detailed way, the problem, its motivation, features and results. Control systems defined by ordinary differential equations are dealt with. Many worked examples have been included. The main focus is on the mathematical aspects of the problem, but some important applications are also described. This book will be suitable as a textbook for advanced university courses, and also as a tool for control theorists and researchers. An extensive list of references is included.
Introduction and some notations - general framework: statement of the problem; motivations and examples; definitions; linear systems; the linearization approach; obstructions to stabilizability; controllability and stabilizability. The Liapunov's direct method: Artstein's theorem; the Jurdjevic-Quinn approach; asymptotic controllability; homogeneous systems; bilinear systems - constant feedback stabilization. Indirect approaches: local approximation; critical cases - the Center Manifold approach; cascade systems; exact and partial linearization; minimum phase systems. Low-dimensional systems.