Using Algebraic Geometry

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.

To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas.