Symmetries and semi-invariants in the analysis of nonlinear systems
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書誌事項
Symmetries and semi-invariants in the analysis of nonlinear systems
Springer, 2011
- hbk.
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注記
Includes references and index
内容説明・目次
内容説明
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.
目次
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.
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