Algebraic Methods for Nonlinear Control Systems. Theory and Applications, 2nd Edition

A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. Algebraic Methods for Nonlinear Control Systems develops a linear-algebraic alternative to the usual differential-geometric approach to nonlinear control, using vector spaces over suitable fields of nonlinear functions. It describes a range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast for the linear-algebraic setting; discussion and solution of basic feedback problems; results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily in the algebraic framework. The second edition has been completely revised with new text, examples and exercises; it is divided into two parts: necessary methodology and applications to control problems. Contents: Part I: Methodology.- Preliminaries.- Modeling.- Accessibility.- Observability.- Systems Structure and Inversion.- System Transformations.- Part II: Applications to Control Problems.- Input−Output Linearization.- Noninteracting Control.- Input−State Linearization.- Disturbance Decoupling.- Model Matching.-Measured Output Feedback Control Problems.