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

... 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)