This book details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the tools for this, such as first-integrals or orbital symmetries, together with rmal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion. The theory is developed for general nlinear systems and specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a different, less complex and more easily comprehensible manner. They are applied to physically motivated systems, to demonstrate how much insight into kwn properties is gained using these techniques. Various control systems applications of the techniques are characterized including: computation of the flow of nlinear systems; computation of semi-invariants; computation of Lyapuv functions for stability analysis and observer design.
Antonio Tornambe is a professor and Laura Menini is an associate professor, both in the area Automatica , which covers both control Theory and robotics. Both of them have been involved in research in those fields generally and, of particular relevance to this book, they have worked on observer design for nonlinear systems (possibly subject to impulsive effects), on stabilization and tracking by state feedback for nonlinear systems, on modeling and control of mechanical systems (possibly subject to impacts), and on control of Hamiltonian systems. They also have wide experience of teaching and their main motivation for writing this book is that of collecting some recent results on the analysis of nonlinear systems, most of them hitherto unpublished, in the mathematical framework that allows both their rigorous derivation and a deep understanding of their meaning and their applicability.