Abstracts Category : Other

Output Stability Analysis for Nonlinear Systems with Time Delays

by Kankanamalage Hasala Gallolu

Systems with time delays have a broad range of applications not only in controlsystems but also in many other disciplines such as mathematical biology, financialeconomics, etc. The time delays cause more complex behaviours of the systems. Itrequires more sophisticated analysis due to the infinite dimensional structure of thespace spaces. In this thesis we investigate stability properties associated with outputfunctions of delay systems.Our primary target is the equivalent Lyapunov characterization of input-tooutputstability (ios). A main approach used in this work is the Lyapuno Krasovskiifunctional method. The Lyapunov characterization of the so called output-Lagrangestability is technically the backbone of this work, as it induces a Lyapunov descriptionfor all the other output stability properties, in particular for ios. In the study, weconsider two types of output functions. The first type is defined in between Banachspaces, whereas the second type is defined between Euclidean spaces. The Lyapunovcharacterization for the first type of output maps provides equivalence between thestability properties and the existence of the Lyapunov-Krasovskii functionals. On theother hand, as a special case of the first type, the second type output renders flexible Lyapunov descriptions that are more efficient in applications. In the special casewhen the output variables represent the complete collection of the state variables,our Lyapunov work lead to Lyapunov characterizations of iss, complementing thecurrent iss theory with some novel results.We also aim at understanding how output stability are affected by the initialdata and the external signals. Since the output variables are in general not a fullcollection of the state variables, the overshoots and decay properties may be affectedin different ways by the initial data of either the state variables or just only the outputvariables. Accordingly, there are different ways of defining notions on output stability,making them mathematically precisely. After presenting the definitions, we explorethe connections of these notions. Understanding the relation among the notions isnot only mathematically necessary, it also provides guidelines in system control anddesign. 2017 Degree granted: Dissertation (Ph.D.) FloridaAtlanticUniversity, 2017. Collection: FAUAdvisors/Committee Members: Wang, Yuan Dr. (Thesis advisor), Charles E. Schmidt College of Science (Degree grantor).