Analysis and Control of Nonlinear Systems

Introduction.- Part II: THEORY.- Introduction to Differential Geometry.- Introduction to Dynamical Systems.- Controlled Systems, Controllability.- Jets of Infinite Order, Lie-Backlund's Equivalence.- Differentially Flat Systems.- Flatness and Motion Planning.- Flatness and Tracking.- Part II: APPLICATIONS.- DC Motor Starting Phase.- Displacements of a Linear Motor With Oscillating Masses.- Synchronization of a Pair of Independent Windshield Wipers.- Control of Magnetic Bearings.- Automatic Flight Control Systems.- References.- Index

From the reviews:

"This book is focused mainly on the analysis of so-called nonlinear flat systems. ... The book is published in the mathematical engineering series, and as a consequence the differential geometry content is presented in a very accessible applied mathematics way." (Guy Jumarie, Zentralblatt MATH, Vol. 1167, 2009)

"This book provides an introduction to the theory of deterministic, continuous-time, finite-dimensional, nonlinear control systems from the particular 'differential-algebraic' point of view, with the notion of 'flatness' as the fundamental underlying principle. ... this book is the first extensive treatment of the notion of flatness in monograph form. As such, it is certainly a useful addition to the control-theory literature. A particular strength of the book is its detailed treatment of many examples ... ." (Kevin A. Grasse, Mathematical Reviews, Issue 2011 j)