Dissertation
Convex Sets of Stable Matrices
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000005318
Abstract
A complex matrix is positive (negative) stable if all its eigenvalues lie in the open right (left) half plane. Stable matrices play a central role in the study of systems of differential equations. In this thesis, we will study the stability of the product and Kronecker product of two or more matrices. We will explore the stability of a principal pivot transform and the Cayley transform of a stable matrix and state sufficient conditions that ensure the stability of these transforms. In addition, we obtain a result about the spectrum of rank-one updated matrix. Furthermore, we shall discuss the stability of convex hulls of stable matrices. Finally, we present some results about the existence of a positive eigenvalue based on the concept of pointed cones, then we generalize these results to characterize P−matrices, copositive matrices, and stable matrices.
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Details
- Title
- Convex Sets of Stable Matrices
- Creators
- Wail Alahmadi
- Contributors
- Michael Tsatsomeros (Advisor)Judith McDonald (Committee Member)Nikolaos K. Voulgarakis (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 102
- Identifiers
- 99901031140501842
- Language
- English
- Resource Type
- Dissertation