@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}
}
@unpublished{GeiselhartGielenLazaretal.2013,
  author    = {Geiselhart, Roman and Gielen, Rob H. and Lazar, Mircea and Wirth, Fabian R.},
  title     = {An Alternative Converse Lyapunov Theorem for Discrete-Time Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-78512},
  year      = {2013},
  abstract  = {This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and semi-global practical Lyapunov functions for globally asymptotically stable systems. Furthermore, for specific classes of sys- tems, the developed converse theorem can be used to establish non-conservatism of a particular type of Lyapunov functions. Most notably, a proof that conewise linear Lyapunov functions are non-conservative for GES conewise linear systems is given and, as a by-product, tractable construction of polyhedral Lyapunov functions for linear systems is attained.},
  subject      = {Ljapunov-Funktion},
  language  = {en}
}