Overview
Most results are derived for continuous- and discrete-time systems showing readers how to recognises when their own techniques are valid in both cases
Rigorous mathematical treatment in a simple style allows in-depth understanding to be easily acquired
Self-contained presentation requires only the most basic of mathematical knowledge of real analysis, linear algebra and systems theory
Includes supplementary material: sn.pub/extras
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Table of contents (8 chapters)
Keywords
About this book
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 normal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion.
The theory is developed for general nonlinear 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 known properties is gained using these techniques. Various control systems applications of the techniques are characterized including: computation of the flow of nonlinear systems; computation of semi-invariants; computation of Lyapunov functions for stability analysis and observer design.
Reviews
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)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Symmetries and Semi-invariants in the Analysis of Nonlinear Systems
Authors: Laura Menini, Antonio Tornambè
DOI: https://doi.org/10.1007/978-0-85729-612-2
Publisher: Springer London
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag London Limited 2011
Hardcover ISBN: 978-0-85729-611-5Published: 08 May 2011
Softcover ISBN: 978-1-4471-6241-4Published: 23 August 2014
eBook ISBN: 978-0-85729-612-2Published: 06 May 2011
Edition Number: 1
Number of Pages: IX, 340
Topics: Control and Systems Theory, Systems Theory, Control, Vibration, Dynamical Systems, Control