Titlebook: Symmetries and Semi-invariants in the Analysis of Nonlinear Systems; Laura Menini,Antonio Tornambè Book 2011 Springer-Verlag London Limite

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Symmetries and Semi-invariants in the Analysis of Nonlinear Systems978-0-85729-612-2

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Book 2011 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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Book 2011fferential 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

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Stability Analysis,with nilpotent but non-zero linear part (confirming the difficulty of distinguishing a center from a focus). Finally, the last sections deal with the use of semi-invariants as elementary bricks for the construction of Lyapunov functions; such methods are developed both for continuous-time and discrete-time systems of arbitrary order.