First Order Linear Systems

<p>A fundamental occupation of a mathematician is to describe a physical situation by a set of equations in order to solve real life problems. Most natural events can be expressed as differential and difference equations. In this respect, <em>Ordinary Differential Equations (ODE)</em> are one of the most useful parts of mathematics for theory and applications.</p> <p>The objective of this project is to study systems of linear differential and difference equations. First, we compare two solution forms for the first order matrix differential equation Y'=AY+YB. The first form, due to Neudecker, utilizes the Kronecker products of matrices to convert an <em>n x n</em> matrix differential equation into an <em>n x n</em> vector ODE. The second form, due to Murty, finds the solution in terms of the fundamental matrix solutions of two n x u vector ODE. This allows dealing with relatively much larger matrices than in Neudecker's solution.</p> <p>Second, we present some basic results on the relation between the<em> k^th</em> order difference equation and the companion matrix equation; these results are not available in the literature. Then, we present a set of necessary and sulfirient conditions for the complete controllability and observability of the general first order difference system. Examples are provided to illustrate many of the theoretical results.</p>

Name thesis:degree_name

Master of Science in Mathematics

Level thesis:degree_level

Thesis (restricted to Georgia Southern)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2004

Author dc:creator

• Tugcu, Gulcin

Contributors dc:contributor

• Donald W. Fausett
• Kanuri N. Murty

• ETD
• Ordinary differential equations
• ODE
• Linear differential equations
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd_legacy/35

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd_legacy-1193