Thesis-1967-Barnett.pdf (5.71 MB)
Solution of some algebraic problems arising in the theory of stability and sensitivity of systems, with particular reference to the Lyapunov matrix equation
thesis
posted on 2018-08-14, 13:21 authored by Stephen BarnettThe matrix equation A'P + PA = -Q arises when the
direct method of Lyapunov is used to analyse the stability of a
constant linear system of differential equations ẋ = Ax. Considerable
attention is given to the solution of this equation for the
symmetric matrix P, given a symmetric positive definite matrix Q.
Several new methods are proposed, including a reduction in the number
of equations and unknowns brought about by introducing a skew-symmetric
matrix; a method based on putting A into Schwarz form
and inverting a triangular matrix; and a solution in terms of a
convergent infinite matrix series. Some numerical experience is
also reported. [Continues.]
History
School
- Science
Department
- Mathematical Sciences
Publisher
© Stephen BarnettPublisher 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
1967Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en