Thesis-1982-Hassan.pdf (3.21 MB)
Extensions of Zubov's method for the determination of domains of attraction
thesis
posted on 2018-05-30, 13:48 authored by Malik A. HassanThis thesis is concerned with the extension of Zubov's
method for the determination of domains of attraction. The
basic definitions and theorems of Liapunov and Zubov as well as
a numerical algorithm (due to White) are given in the introductory
chapter.
The application of the method of Zubov to some practical
situations like power systems and control systems of order two
is the subject of chapter two.
Chapter three describes the determination of the domains
of attraction for scalar time varying systems. The series solution
has a similar problem of non-uniform convergence that occurs in
autonomous systems.
Extension of the method to third order non-linear autonomous
systems is included in Chapter four so that it can be applied to second order time varying system which is described in Chapter
five. Results in the form of slices or cross-sections of the
stability boundaries in the various principal planes are obtained.
Systems which have periodic solutions are examined and the
domain of attraction of the stable limit cycle is determined in
Chapter six. Approximate solutions are also used in trying to
determine the domain of attraction of the periodic solutions.
In Chapter seven a technique for solving global
optimization problems is presented. Several one-dimensional and
two-dimensional minimization problems are solved and the results
indicate the accuracy of this technique.
Funding
Universiti Pertanian Malaysia (Serdang, Malaysia).
History
School
- Science
Department
- Mathematical Sciences
Publisher
© Malik Abu HassanPublisher 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
1982Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en