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SOURCE: Isidori A. Nonlinear Control Systems 3ed 2000
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MEDIAINFO
Textbook in PDF format The purpose of this book is to present a self-contained description of the fundamentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as well as a reference to scientists and engineers involved in the analysis and design of feedback systems. Chapter 1 introduces invariant distributions, a fundamental tool in the analysis of the internal structure of nonlinear systems. With the aid of this concept, it is shown that a nonlinear system locally exhibits decompositions into reachableunreachable parts andor observableunobservable parts, similar to those introduced by Kalman for linear systems. Chapter 2 explains to what extent global decompositions may exist, corresponding to a partition of the whole state space into lower dimensional reachability andor indistinguishability subsets. Chapter 3 describes various formats in which the input-output map of a nonlinear system may be represented, and provides a short description of the fundamentals of realization theory. Chapter 4 illustrates how a series of relevant design problems can be solved for a single-input single-output nonlinear system. It explains how a system can be transformed into a linear and controllable one by means of feedback and coordinates transformation, discusses how the nonlinear analogue of the notion of zero plays an important role in the problem of achieving local asymptotic stability, describes the problems of asymptotic tracking, model matching and disturbance decoupling. The approach is somehow elementary, in that requires only standard mathematical tools. Chapter 5 covers similar subjects for a special class of multivariable nonlinear systems, namely those systems which can be rendered noninteractive by means of static state feedback. For this class of systems, the analysis is a rather straightforward extension of the one illustrated in Chapter 4. Finally, the last two Chapters are devoted to the solution of the problems of output regulation, disturbance decoupling, noninteracting control with stability via static state feedback, and noninteracting control via dynamic feedback, for a broader class of multivariable nonlinear systems. The analysis in these Chapters is mostly based on a number of key differential geometric concepts that, for convenience, are treated separately in Chapter 6
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