Diagonal Riccati Stability and Applications
Alexander Aleksandrov, Oliver Mason
TL;DR
This paper investigates diagonal Riccati stability for matrix pairs, providing a necessary and sufficient condition, and explores applications in generalised Lotka-Volterra systems, contributing to control theory and mathematical biology.
Contribution
It derives a complete characterization of diagonal Riccati stability and applies it to biological and control system models, advancing theoretical understanding.
Findings
Established a necessary and sufficient condition for diagonal Riccati stability.
Applied the stability condition to generalised Lotka-Volterra systems.
Provided insights into stability analysis in biological and control systems.
Abstract
We consider the question of diagonal Riccati stability for a pair of real matrices A, B. A necessary and sufficient condition for diagonal Riccati stability is derived and applications of this to two distinct cases are presented. We also describe some motivations for this question arising in the theory of generalised Lotka-Volterra systems.
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