Thesis-1973-Shields.pdf (4.91 MB)
The behaviour of optimal Lyapunov functions
thesis
posted on 2018-10-31, 15:55 authored by Derek N. ShieldsThe use of Lyapunov's direct method in obtaining regions
of asymptotic stability of non-linear autonomous systems is
well-known. This thesis is an investigation into the optimization
of some function of these systems over different classes
of Lyapunov functions.
In Chapter 2 bounds on the transient response of two
systems are optimized over a subset of quadratic Lyapunov
functions and numerical work is carried out to compare
several bounds.
Zubov's equation is the subject of Chapter 3. The non-uniformity
of the series-construction procedure is studied
analytically and a new approach is made to the solution of
the equation by finite difference methods.
Chapters 4, 5 and 6 have a common theme of optimizing
the RAS over a class of Lyapunov functions. Chapter 4 is
restricted to optimal quadratics which are investigated analytically
and numerically, two algorithms being developed. An
optimal quadratic algorithm and a RAS algorithm are proposed
in Chapter 5 for high order systems. Extensions are made in
Chapter 6 to optimal Lyapunov functions of general degree and
relay control systems and systems of Lur'e form are considered.
History
School
- Science
Department
- Mathematical Sciences
Publisher
© D.N. ShieldsPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
1973Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en