The book is an excellent contribution to nonlinear control theory. Analysis, geometric and asymptotic concepts and their applications to feedback stabilization problems are included. New recursive Lyapunov designs for a wide class of nonlinear systems are proposed. In Chapter 2 of the book the notions of storage function, supply rate, and passivity are defined and the relationship between passivity and Lyapunov stability is established. These concepts are used to analyze stability for parallel and feedback interconnections. This chapter ends with a study of feedback passivity, namely, the possibility of a system being made passive with static feedback. The concept of passivity is one of the main tools for feedback design in the rest of the chapters. In Chapter 3 the notion of stability margin is defined. The stability margin between optimality and passivity is examined. An inverse optimal design based on the existence of control Lyapunov functions is discussed. Inverse optimal design constitutes a systematic approach towards feedback stabilization in the remaining chapters. Chapter 4 offers sufficient conditions for global and semiglobal stabilization of cascade systems. Input-to-state stability, passivity and control Lyapunov functions are used for the analysis. Interesting applications illustrating the nature of the feedback design are included. The peaking phenomenon is discussed and a characterization of a class of nonpeaking cascade systems is presented.
Chapter 5 is the most attractive part of this book. Constructive nonlinear designs for control Lyapunov functions are proposed, guaranteeing feedback stabilization for cascade systems. Two basic constructions are presented: composite Lyapunov functions and Lyapunov functions with a cross-term. The methodology is extended to design stabilizing control for a wide class of systems including cascades with unknown parameters. In Chapter 6 the feedback passivation design, used for cascade systems in previous chapters, is extended to larger classes of nonlinear systems, including those having lower- and upper-triangular structure. Backstepping and forwarding recursive procedures are used. Both procedures construct a passivating output and a storage function to be used as a Lyapunov function.