"Symmetries and Semi-invariants in the Analysis of Nonlinear
Systems" details the analysis of continuous- and discrete-time
dynamical systems described by differential and difference
equations respectively. Differential geometry provides the
essential tools for the analysis, tools such as first-integrals or
orbital symmetries, together with normal forms of vector fields and
of maps. The use of such tools allows the solution of some
important problems, studied in detail in the text, which
includelinearization by state immersionand the computation of
nonlinear superposition formulae for nonlinear systems described by
solvable Lie algebras.
The theory is developed for general nonlinear systems and, in
view of their importance for modeling physical systems, specialized
for the class of Hamiltonian systems. By using the strong geometric
structure of Hamiltonian systems, the results proposed are stated
in a quite different, less complex and more easily comprehensible
manner. Throughout the text the results are illustrated by many
examples, some of them being physically motivated systems, so that
the reader can appreciate how much insight is gained by means of
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.
"Symmetries and Semi-invariants in the Analysis of Nonlinear
Systems" will be of interest to researchers and graduate students
studying control theory, particularly with respect to nonlinear
systems. All the necessary background and mathematical derivations
are related in detail but in a simple writing style that makes the
book accessible in depth to readers having a standard knowledge of
real analysis, linear algebra and systems theory. "
General
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