@phdthesis{Schoenlein2012,
  author    = {Sch{\"o}nlein, Michael},
  title     = {Stability and Robustness of Fluid Networks: A Lyapunov Perspective},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-72235},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {In the verification of positive Harris recurrence of multiclass queueing networks the stability analysis for the class of fluid networks is of vital interest. This thesis addresses stability of fluid networks from a Lyapunov point of view. In particular, the focus is on converse Lyapunov theorems. To gain an unified approach the considerations are based on generic properties that fluid networks under widely used disciplines have in common. It is shown that the class of closed generic fluid network models (closed GFNs) is too wide to provide a reasonable Lyapunov theory. To overcome this fact the class of strict generic fluid network models (strict GFNs) is introduced. In this class it is required that closed GFNs satisfy additionally a concatenation and a lower semicontinuity condition. We show that for strict GFNs a converse Lyapunov theorem is true which provides a continuous Lyapunov function. Moreover, it is shown that for strict GFNs satisfying a trajectory estimate a smooth converse Lyapunov theorem holds. To see that widely used queueing disciplines fulfill the additional conditions, fluid networks are considered from a differential inclusions perspective. Within this approach it turns out that fluid networks under general work-conserving, priority and proportional processor-sharing disciplines define strict GFNs. Furthermore, we provide an alternative proof for the fact that the Markov process underlying a multiclass queueing network is positive Harris recurrent if the associate fluid network defining a strict GFN is stable. The proof explicitely uses the Lyapunov function admitted by the stable strict GFN. Also, the differential inclusions approach shows that first-in-first-out disciplines play a special role.},
  subject      = {Warteschlangennetz},
  language  = {en}
}
@article{AlmeidaHristovaDashkovskiy2021,
  author    = {Almeida, R. and Hristova, S. and Dashkovskiy, S.},
  title     = {Uniform bounded input bounded output stability of fractional-order delay nonlinear systems with input},
  series = {International Journal of Robust and Nonlinear Control},
  volume    = {31},
  journal   = {International Journal of Robust and Nonlinear Control},
  number    = {1},
  doi       = {10.1002/rnc.5273},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-218554},
  pages     = {225 -- 249},
  year      = {2021},
  abstract  = {The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time-varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.},
  language  = {en}
}