Date of Award

1-12-2006

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Mihaly Bakonyi - Chair

Second Advisor

Andrey Shilnikov

Third Advisor

Michael Stewart

Abstract

In the first part of the thesis we present several interior point algorithms for solving certain positive definite programming problems. One of the algorithms is adapted for finding out whether there exists or not a positive definite matrix which is a real linear combination of some given symmetric matrices A1,A2, . . . ,Am. In the second part of the thesis we discuss stability of nonlinear dynamical systems. We search using algorithms described in the first part, for Lyapunov functions of a few forms. A suitable Lyapunov function implies the existence of a hyperellipsoidal attraction region for the dynamical system, thus guaranteeing stability.

Included in

Mathematics Commons

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