@phdthesis{Geiselhart2015,
  author    = {Geiselhart, Roman},
  title     = {Advances in the stability analysis of large-scale discrete-time systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-112963},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Several aspects of the stability analysis of large-scale discrete-time systems are considered. An important feature is that the right-hand side does not have have to be continuous. In particular, constructive approaches to compute Lyapunov functions are derived and applied to several system classes. For large-scale systems, which are considered as an interconnection of smaller subsystems, we derive a new class of small-gain results, which do not require the subsystems to be robust in some sense. Moreover, we do not only study sufficiency of the conditions, but rather state an assumption under which these conditions are also necessary. Moreover, gain construction methods are derived for several types of aggregation, quantifying how large a prescribed set of interconnection gains can be in order that a small-gain condition holds.},
  subject      = {Ljapunov-Funktion},
  language  = {en}
}