@phdthesis{Zilker2019,
  author    = {Zilker, Markus},
  title     = {The stability of finished pharmaceutical products and drug substances beyond their labeled expiry dates},
  doi       = {10.25972/OPUS-18069},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-180695},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {Upon approval of a drug, the stability of the API and the FPP has to be studied intensively because it determines the shelf-life. If a drug is found to be stable, the expiry date is arbitrary set to five years at the maximum, if a drug tends to undergo degradation, the expiry date is set shorter. The drug product must comply with predefined specifications in accordance with the ICH guidelines Q6A and Q6B during its entire market life. The content of the active substance is required to be within a specification of 95-105\% of its labeled claim until expiry corresponding to the ICH guideline Q1A(R2). However, there is little or scattered literature information addressing the stability of drug products beyond their expiry dates. The objective of this thesis was to study and assess the long-term stability of a collection involving numerous pure drug substances and ampoules manufactured in the 20th century. The content and the impurity profile were examined by means of appropriate analytical methods, mainly using liquid chromatography. The results were compared to data being available in the literature. Assessing the stability regarding the dosage form and the affiliation of the drug class was conducted. The experimental studies comprise the examination of 50 drug substances manufactured 20-30 years ago and 14 long expired ampoules which were older than 40 years in the time of analysis, exceeding many times the maximum shelf life of five years. For investigation of the solid drug substances, pharmacopoeial methods were applied as far as possible. Indeed, results of the study showed that 44 tested substances still complied with the specification of the Ph. Eur. with regard to the content and impurity profile, even after more than two decades of storage. For analysis of the injection solutions, HPLC-UV and HPLC-ESI/MS techniques were applied, commonly based on liquid chromatography methods of the Ph. Eur. for determination of related substances. Each method was further validated for its application to ensure accurate API quantification corresponding to ICH Q2(R1). Quite a few ampoules were identified to show surprisingly high stability. In spite of their age of 53-72 years, APIs such as caffeine, etilefrine, synephrine, metamizole sodium, furosemide, and sodium salicylate complied with the specified content that is valid nowadays, respectively. Nevertheless, typical degradation reaction, e.g. hydrolysis, oxidation, or isomerization, was observed in all remaining ampoules. Various degrees of hydrolysis were revealed for scopolamine, procaine, and adenosine triphosphate, the contents were decreased to 71\%, 70\%, and 15\% of the declared concentrations, respectively. In the epinephrine and dipyridamole ampoules, oxidative degradation has been occurred, finding respective API contents of more or less 70\%. For dihydroergotamine, excessive decomposition by epimerization was observed, resulting in an API content of 21\% and degradation by isomerization was found in lobeline, still containing 64\% of the labeled claim. In conclusion, supported by the data of the present studies and the literature, defining and authorizing a longer shelf-life may be applicable to numerous pharmaceuticals which should be considered by pharmaceutical manufacturers and regulatory authorities, if justified based on stability studies. A general extension of the shelf-lives of drug products and the abolishment or extension of the maximum shelf-life limit of five years would prevent disposing of still potent medications and save a lot of money to the entire health care system.},
  subject      = {Stabilit{\"a}t},
  language  = {en}
}
@phdthesis{Unger2020,
  author    = {Unger, Nina},
  title     = {Stability of Tryptophan in Parenteral Amino Acid Solutions: Identification of Degradation Products and Development of HPLC Analysis Methods},
  doi       = {10.25972/OPUS-19982},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-199825},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {The stability of Trp in pure solutions and in parenteral AA formulations was evaluated with regard to typically used manufacturing processes, storage conditions and primary packaging. Therefore, thorough stability studies on Trp solutions were conducted beforehand. The applied stressing method, i.e. steam sterilization by autoclave, are chemically seen relatively mild but showed to be efficient to induce Trp degradation in the presence of oxygen. Subsequent identification, separation and characterization were challenging due to similar substance properties, numerous stereoisomers and pairs of diastereomers found amongst them. However, the identified o-aminoacetophenone compounds, Kyn and NFK, are associated with photo reactivity and have photo-oxidizing properties. Thus, best possible protection from UV-light, together with strict oxygen expulsion, are the most important criteria to impede Trp degradation after autoclaving. The identification of Trp degradation products was assisted by the compilation of a substance library, which included manifold reported and chemically plausible Trp degradation substances. The substances were classified for priority and their early or late-stage occurrence. The large number of possible substances and stereoisomers was narrowed down with the information retrieved from LC-UV/MS experiments. However, final identification was achieved by the synthesis of proposed substances as references. The following eight substances were characterized as Trp degradation substances: Kyn, NFK and three pairs of diastereomers R,R/R,S DiOia, R,R/R,S Oia and cis/trans PIC. Fig. 33 shows the proposed degradation pathway and demonstrates the close chemical relationship, which may be an explanation for the conversion of some substances into each other during the storage period. The proposed pathway brings together the results of different Trp stability and stressing studies, respectively [89, 94, 97, 98, 103, 133]. To our knowledge, the simultaneous formation of the identified degradation substances has not been reported before and especially not under the stressing conditions applied. The application of a traditional RP-HPLC method was compared to two developed IP-HPLC methods and a RP-HPLC methods using a modified perfluorinated column. Orthogonal analyses methods and especially the combination of UV and MS detection are necessary in order to indicate potentially undetected degradation substances. Main evaluation criteria were the separation performance, analyses time, reproducibility and feasibility. The best results upon assessment of all Trp degradation products, in both; pure Trp solutions and pharmaceutical formulations, were obtained by a traditional RP-HPLC. The optimized method was validated according to ICH guidelines Q2(R1) and meets the criteria of a stability-indicating HPLC-UV method. The validated method has a sufficient separation performance with an adequate selectivity indicating the Trp degradation substances next to each other and next to other AAs in finished pharmaceutical formulations. The detailed knowledge of Trp degradation and the method presented may be transferred practically to the pharmaceutical industry processing Trp-containing products. In general, the findings might contribute to the quality management of such pharmaceutical products during manufacturing and storage. Additionally, the study results provide basic information for the establishment of an impurity consideration following the ICH guidelines Q3B (R2) (impurities in new drug products) for products containing Trp. However, further development of the method applying more sophisticated detectors or more potent HPLC techniques like e.g. UHPLC and the implication of more sensitive (MS) detectors like ToF-MS would be advantageous with regard to economic and practical aspects.},
  subject      = {Stabilit{\"a}t},
  language  = {en}
}
@phdthesis{Suttner2020,
  author    = {Suttner, Raik},
  title     = {Output Optimization by Lie Bracket Approximations},
  doi       = {10.25972/OPUS-21177},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211776},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {In this dissertation, we develop and analyze novel optimizing feedback laws for control-affine systems with real-valued state-dependent output (or objective) functions. Given a control-affine system, our goal is to derive an output-feedback law that asymptotically stabilizes the closed-loop system around states at which the output function attains a minimum value. The control strategy has to be designed in such a way that an implementation only requires real-time measurements of the output value. Additional information, like the current system state or the gradient vector of the output function, is not assumed to be known. A method that meets all these criteria is called an extremum seeking control law. We follow a recently established approach to extremum seeking control, which is based on approximations of Lie brackets. For this purpose, the measured output is modulated by suitable highly oscillatory signals and is then fed back into the system. Averaging techniques for control-affine systems with highly oscillatory inputs reveal that the closed-loop system is driven, at least approximately, into the directions of certain Lie brackets. A suitable design of the control law ensures that these Lie brackets point into descent directions of the output function. Under suitable assumptions, this method leads to the effect that minima of the output function are practically uniformly asymptotically stable for the closed-loop system. The present document extends and improves this approach in various ways. One of the novelties is a control strategy that does not only lead to practical asymptotic stability, but in fact to asymptotic and even exponential stability. In this context, we focus on the application of distance-based formation control in autonomous multi-agent system in which only distance measurements are available. This means that the target formations as well as the sensed variables are determined by distances. We propose a fully distributed control law, which only involves distance measurements for each individual agent to stabilize a desired formation shape, while a storage of measured data is not required. The approach is applicable to point agents in the Euclidean space of arbitrary (but finite) dimension. Under the assumption of infinitesimal rigidity of the target formations, we show that the proposed control law induces local uniform asymptotic (and even exponential) stability. A similar statement is also derived for nonholonomic unicycle agents with all-to-all communication. We also show how the findings can be used to solve extremum seeking control problems. Another contribution is an extremum seeking control law with an adaptive dither signal. We present an output-feedback law that steers a fully actuated control-affine system with general drift vector field to a minimum of the output function. A key novelty of the approach is an adaptive choice of the frequency parameter. In this way, the task of determining a sufficiently large frequency parameter becomes obsolete. The adaptive choice of the frequency parameter also prevents finite escape times in the presence of a drift. The proposed control law does not only lead to convergence into a neighborhood of a minimum, but leads to exact convergence. For the case of an output function with a global minimum and no other critical point, we prove global convergence. Finally, we present an extremum seeking control law for a class of nonholonomic systems. A detailed averaging analysis reveals that the closed-loop system is driven approximately into descent directions of the output function along Lie brackets of the control vector fields. Those descent directions also originate from an approximation of suitably chosen Lie brackets. This requires a two-fold approximation of Lie brackets on different time scales. The proposed method can lead to practical asymptotic stability even if the control vector fields do not span the entire tangent space. It suffices instead that the tangent space is spanned by the elements in the Lie algebra generated by the control vector fields. This novel feature extends extremum seeking by Lie bracket approximations from the class of fully actuated systems to a larger class of nonholonomic systems.},
  subject      = {Extremwertregelung},
  language  = {en}
}
@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}
}
@phdthesis{Sapozhnikova2018,
  author    = {Sapozhnikova, Kateryna},
  title     = {Robust Stability of Differential Equations with Maximum},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-173945},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {In this thesis stability and robustness properties of systems of functional differential equations which dynamics depends on the maximum of a solution over a prehistory time interval is studied. Max-operator is analyzed and it is proved that due to its presence such kind of systems are particular case of state dependent delay differential equations with piecewise continuous delay function. They are nonlinear, infinite-dimensional and may reduce to one-dimensional along its solution. Stability analysis with respect to input is accomplished by trajectory estimate and via averaging method. Numerical method is proposed.},
  subject      = {Differentialgleichung},
  language  = {en}
}
@misc{Proell2013,
  type      = {Master Thesis},
  author    = {Pr{\"o}ll, Sebastian},
  title     = {Stability of Switched Epidemiological Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-108573},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {In this thesis it is shown how the spread of infectious diseases can be described via mathematical models that show the dynamic behavior of epidemics. Ordinary differential equations are used for the modeling process. SIR and SIRS models are distinguished, depending on whether a disease confers immunity to individuals after recovery or not. There are characteristic parameters for each disease like the infection rate or the recovery rate. These parameters indicate how aggressive a disease acts and how long it takes for an individual to recover, respectively. In general the parameters are time-varying and depend on population groups. For this reason, models with multiple subgroups are introduced, and switched systems are used to carry out time-variant parameters. When investigating such models, the so called disease-free equilibrium is of interest, where no infectives appear within the population. The question is whether there are conditions, under which this equilibrium is stable. Necessary mathematical tools for the stability analysis are presented. The theory of ordinary differential equations, including Lyapunov stability theory, is fundamental. Moreover, convex and nonsmooth analysis, positive systems and differential inclusions are introduced. With these tools, sufficient conditions are given for the disease-free equilibrium of SIS, SIR and SIRS systems to be asymptotically stable.},
  subject      = {Gew{\"o}hnliche Differentialgleichung},
  language  = {en}
}