Symmetries and Semi-invariants in the Analysis of Nonlinear Systems

Antonio Tornambè 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writing this book is that of collecting some recent results on the analysis of nonlinear systems, most of them hitherto unpublished, in the mathematical framework that allows both their rigorous derivation and a deep understanding of their meaning and their applicability.

• Part I: Theory.- Introduction.- Notation and Background.- Analysis of Linear Systems.- Analysis of Nonlinear Systems.- Analysis of Hamiltonian Systems.- Linearization by State Immersion.- Linearization by State Immersion of Hamiltonian Systems.- Extensions Based on the Use of Orbital Symmetries.- Part II: Applications to Control Systems.- Computation of the Flow of Linearizable Systems.- Semi-invariants.- Stability Analysis.- Observer Design.- Exact Sampling of Continuous-time Systems.- Applications to Physically Motivated Systems.

From the reviews:“The book Symmetries and semi-invariants in the analysis of nonlinear systems deals with some useful techniques to analyze the qualitative behavior of both continuous and discrete finite-dimensional dynamical systems. … It is written very clearly, is basically self-contained, and a large number of exercises and examples are included. In summary, the book is highly recommended for all who work in dynamical systems, especially when the concept of symmetry plays an essential role.” (Isaac A. García, Mathematical Reviews, January, 2014)