Nonlinear Systems Analysis

THIS IS a completely rewritten version of the first edition which appeared in 1978. At that time the book gave a good overview of the main body of nonlinear systems and control theory, except for nonlinear optimal control theory. The emphasis was very much on the analysis of systems (in openor closed-loop configuration), instead of on the actual design of controllers. Most attention was being focused on stability issues, both from the input-output and the state-space point of view. Highlights in this theory were the concepts of input-output stability including Popov's criterion and the circle criterion (see also Desoer and Vidyasagar, 1975), the theory of Lyapunov stability, and perhaps the method of describing functions. Since the appearance of the first edition, geometric nonlinear control theory has become a prevailing trend. (In fact these developments were already initiated at the beginning of the seventies.) Geometric nonlinear control theory started as a successful approach to deal with basic system-theoretic questions in the state-space formulation of nonlinear control systems, such as controllability and observability properties and minimal realization theory. It gained strong impetus at the beginning of the eighties by the systematic study of nonlinear (state) feedback for various synthesis problems; also stimulated by the geometric approach to linear control theory of Wonham and Morse and Basile and Marro: In particular the Lie bracket conditions for controllability and feedback linearizability have become popular and powerful tools in nonlinear control. The books by Isidori (1989) and Nijmeijer and Van der Schaft (1990) are clear exponents of the achievements of geometric nonlinear control theory. In the last couple of years one can witness some developments which can be looked at as attempts to bridge the gap between nonlinear systems and control theory as put forward in the first edition of the present book on the one hand, and geometric nonlinear control theory on the other hand. Indeed, in nonlinear adaptive control as well as in nonlinear robust control (including nonlinear ~-cont ro l ) there is much need for the kind of stability concepts as exposed in the first edition of the book, while at the same time geometric nonlinear control theory offers an underlying structural framework. In particular passivity, and more generally, dissipativity concepts turn out to be extremely useful in these areas, especially within the context of the control of physical systems. Also, there has been recently some rapprochement between nonlinear input-output theory and (geometric) state-space theory. In my opinion these converging developments are very important and indeed offer promising perspectives for a truly nonlinear control design. In the present second edition Professor Vidyasagar has made an admirable attempt to include at least an introduction to geometric nonlinear control theory in an additional chapter of the book. In fact, this new chapter deals with the perhaps most 'useful' parts of geometric nonlinear control theory such as controllability, feedback linearization and input-output linearization. The other most noticeable differences with the first edition are the inclusion of some