The primary aim of this revised and expanded second edition of the author’s 1978 book [1] remains the same: providing engineers with a rigorous introduction to nonlinear systems analysis. The book should also appeal to applied mathematicians and computer scientists interested in nonlinear systems. It can be used as a textbook, but should also be valuable as a reference.

The well-written introduction and chapter 2 present the basic material on nonlinear systems of ordinary differential equations that should be familiar to readers. The remaining five chapters utilize the background without referring to it repeatedly. Chapter 3 introduces the analysis of autonomous second-order systems and especially of periodic solutions and their approximation. This discussion continues in chapter 4 with some further methods for the approximate analysis of solutions, including the use of singular perturbations. Chapter 5 turns to one of the fundamental topics of control and systems theory, namely Lyapunov stability. Various new results have been included in this second edition, such as observer/controller stabilization of nonlinear systems and relationships between Lyapunov stability and input/output stability. Chapter 6 introduces the more recent input/output stability theory. Again, the author has made several additions, such as some results on feedback stability and, in chapters 5 and 6, material on discrete-time systems. Finally, chapter 7, on differential geometric methods, is new. The use of these methods in the design of nonlinear control systems has advanced considerably since the first edition appeared, and I commend the author for providing an introduction to this area. By necessity, the theory had to be restricted to a local analysis, but the presentation does address such topics as reachability, observability, feedback linearization, and the stabilization of linearizable systems. The book ends with three new appendices covering details of several theoretical results.

The examples in the first edition were mostly simple exercises. It is noteworthy that several larger applications have been included throughout the text, most of them related to robotics problems. At the same time, little material is included on numerical techniques for solving practical problems in this area, but clearly any meaningful discussion of such computational methods would have extended the length of the book excessively.

All in all, this work represents a fine new version of an already well-established book that should serve its intended purpose well.