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Symmetries and Semi-invariants in the Analysis of Nonlinear Systems (Paperback, 2011 ed.)
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Symmetries and Semi-invariants in the Analysis of Nonlinear Systems (Paperback, 2011 ed.)
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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.
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