DSpace Collection:https://dspace.lboro.ac.uk/2134/46422018-06-23T06:21:25Z2018-06-23T06:21:25ZEquivalence transformations in linear systems theoryFretwell, Paulhttps://dspace.lboro.ac.uk/2134/332592018-06-01T10:42:33Z1986-01-01T00:00:00ZTitle: Equivalence transformations in linear systems theory
Authors: Fretwell, Paul
Abstract: There is growing interest in infinite frequency structure of
linear systems, and transformations preserving this type of
structure. Most work has been centred around Generalised
State Space (GSS) systems. Two constant equivalence
transformations for such systems are Rosenbrock's Restricted
System Equivalence (RSE) and Verghese's Strong
Equivalence (str.eq.). Both preserve finite and infinite
frequency system structure. RSE is over restrictive in
that it is constrained to act between systems of the same
dimension. While overcoming this basic difficulty str.eq.
on the other hand has no closed form description. In this
work all these difficulties have been overcome. A constant
pencil transformation termed Complete Equivalence (CE) is
proposed, this preserves finite elementary divisors and
non-unity infinite elementary divisors. Applied to GSS
systems CE yields Complete System Equivalence (CSE)
which is shown to be a closed form description of str.eq.
and is more general than RSE as it relates systems of
different dimensions.
Equivalence can be described in terms of mappings of the
solution sets of the describing differential equations
together with mappings of the constrained initial
conditions. This provides a conceptually pleasing
definition of equivalence. The new equivalence is termed
Fundamental Equivalence (FE) and CSE is shown to be a
matrix characterisation of it.
A polynomial system matrix transformation termed Full
Equivalence (fll.e.) is proposed. This relates general
matrix polynomials of different dimensions while preserving
finite and infinite frequency structure. A definition of
infinite zeros is also proposed along with a generalisation
of the concept of infinite elementary divisors (IED) from
matrix pencils to general polynomial matrices. The IED provide an additional method of dealing with infinite zeros.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.1986-01-01T00:00:00ZPolynomial matrices associated with linear constant multivariable delay-differential systemsFrost, M.G.https://dspace.lboro.ac.uk/2134/332572018-06-01T10:35:28Z1979-01-01T00:00:00ZTitle: Polynomial matrices associated with linear constant multivariable delay-differential systems
Authors: Frost, M.G.
Abstract: Matrices which can be identified as system matrices
corresponding to (linear constant) multivariable delay-differential systems
are considered. These matrices are extensions of the state-space and
polynomial system matrices which are encountered in connection with
multivariable ordinary differential systems. Whereas these latter matrices
have elements which are polynomials in one variable, the matrices
considered have elements which are polynomials in two or more variables.
The matrices considered are treated in two ways. In the first
approach the results available for matrices corresponding to ordinary
differential systems can be readily extended to results for those
corresponding to delay-differential systems. However, the main intention
is to consider the extension of results without using this approach.
Several results are in fact established for the matrices under consideration.
Many of these results involve the new concept of zeros of matrices of the
form considered.
Although the second approach to these matrices is treated
initially as a purely mathematical exercise, it is then shown that there
is some physical justification for this approach. This is done by
consideration of results concerning the controllability of delay differential
systems. In fact, the question of controllability of such
systems is considered in some detail, not simply with a view to justification
of the preceding results. The concept of observability is also considered,
but not in the same detail.
In the concluding chapter another type of system matrix which can be used in the treatment of delay differential systems is
considered. Such a matrix is considered in the context of the results
obtained in the preceding chapters, and the connections between the
results given for this form of system matrix and results previously
obtained are examined. Again the concepts of controllability and
observability are considered.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.1979-01-01T00:00:00ZArtificial intelligence and simulations applied to interatomic potentialsHobday, Stevenhttps://dspace.lboro.ac.uk/2134/332552018-06-01T10:14:17Z1998-01-01T00:00:00ZTitle: Artificial intelligence and simulations applied to interatomic potentials
Authors: Hobday, Steven
Abstract: The interatomic potential is a mathematical model that describes the chemistry occurring at the atomic
level. It provides a functional mapping between the atomic nuclei coordinates and the total potential
energy of a system. This thesis investigates three aspects of interatomic potentials, the first of
which is the simulation of materials at the atomic scale using classical molecular dynamics (MD). Molecular dynamics code is used to follow the evolution of a system of discrete particles through
time and is employed here to model the bombardment of fullerite films modified with low dose Argon ion impacts. [Continues.]
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.1998-01-01T00:00:00ZComputing oscillatory integrals by complex methodsChung, Kwok-Chiuhttps://dspace.lboro.ac.uk/2134/332392018-05-31T14:56:24Z1998-01-01T00:00:00ZTitle: Computing oscillatory integrals by complex methods
Authors: Chung, Kwok-Chiu
Abstract: The research is concerned with the proposal and the development of a general
method for computing rapidly oscillatory integrals with sine and cosine weight
integrands of the form f(x) exp(iωq(x)). In this method the interval (finite
or infinite) of integration is transformed to an equivalent contour in the complex
plane and consequently the problem of evaluating the original oscillatory
integral reduces to the evaluation of one or more contour integrals. Special
contours, called the optimal contours, are devised and used so that the resulting
real integrals are non-oscillatory and have rapidly decreasing integrands
towards one end of the integration range. The resulting real integrals are then
easily computed using any general-purpose quadrature rule. [Continues.]
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.1998-01-01T00:00:00Z