Asymptotic behavior of dynamical and control systems under perturbation and discretization / Lars Grüne

Auteur: Grüne, Lars (1967-.) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1783Langue: anglaisÉditeur: Berlin : Springer, 2002 ISBN: 9783540433910 Note: ... After the introduction and the preparatory Chapter 2 (mainly on the considered systems classes), Chapters 3 and 4 study attracting sets. Here the new concept of dynamical Input-to-State-Stability is central. In Chapter 5 the connection between time and space dicretization on the one hand and disturbed systems on the other is established. Thus the theory developed in Chapters 3 and 4 becomes applicable to the analysis of numerical methods. This is performed in detail in Chapter 6 for attracting sets and for attractors. In Chapter 7 domains of attraction and reachable sets are discussed. The text is completed by 3 appendices: on viscosity solutions, on comparison functions and on numerical examples; finally, it contains a list of notation, a subject index and 129 references. ... (Zentralblatt) Sujets MSC: 65P40 Numerical analysis -- Numerical problems in dynamical systems -- Nonlinear stabilities
37B25 Dynamical systems and ergodic theory -- Topological dynamics -- Lyapunov functions and stability; attractors, repellers
93D30 Systems theory; control -- Stability -- Scalar and vector Lyapunov functions
34D45 Ordinary differential equations -- Stability theory -- Attractors
37Mxx Dynamical systems and ergodic theory -- Approximation methods and numerical treatment of dynamical systems
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... After the introduction and the preparatory Chapter 2 (mainly on the considered systems classes), Chapters 3 and 4 study attracting sets. Here the new concept of dynamical Input-to-State-Stability is central. In Chapter 5 the connection between time and space dicretization on the one hand and disturbed systems on the other is established. Thus the theory developed in Chapters 3 and 4 becomes applicable to the analysis of numerical methods. This is performed in detail in Chapter 6 for attracting sets and for attractors. In Chapter 7 domains of attraction and reachable sets are discussed. The text is completed by 3 appendices: on viscosity solutions, on comparison functions and on numerical examples; finally, it contains a list of notation, a subject index and 129 references. ... (Zentralblatt)

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