Systems with time delays have a broad range of applications not only in control
systems but also in many other disciplines such as mathematical biology, financial
economics, etc. The time delays cause more complex behaviours of the systems. It
requires more sophisticated analysis due to the infinite dimensional structure of the
space spaces. In this thesis we investigate stability properties associated with output
functions of delay systems.
Our primary target is the equivalent Lyapunov characterization of input-tooutput
stability (ios). A main approach used in this work is the Lyapuno Krasovskii
functional method. The Lyapunov characterization of the so called output-Lagrange
stability is technically the backbone of this work, as it induces a Lyapunov description
for all the other output stability properties, in particular for ios. In the study, we
consider two types of output functions. The first type is defined in between Banach
spaces, whereas the second type is defined between Euclidean spaces. The Lyapunov
characterization for the first type of output maps provides equivalence between the
stability properties and the existence of the Lyapunov-Krasovskii functionals. On the
other 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 case
when the output variables represent the complete collection of the state variables,
our Lyapunov work lead to Lyapunov characterizations of iss, complementing the
current iss theory with some novel results.
We also aim at understanding how output stability are affected by the initial
data and the external signals. Since the output variables are in general not a full
collection of the state variables, the overshoots and decay properties may be affected
in different ways by the initial data of either the state variables or just only the output
variables. Accordingly, there are different ways of defining notions on output stability,
making them mathematically precisely. After presenting the definitions, we explore
the connections of these notions. Understanding the relation among the notions is
not only mathematically necessary, it also provides guidelines in system control and
design. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_38017 |
| Contributors | Gallolu Kankanamalage, Hasala Senpathy (author), Wang, Yuan (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation, Text |
| Format | 143 p., application/pdf |
| Rights | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder., http://rightsstatements.org/vocab/InC/1.0/ |
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