On the phases of a regular linear relation

Abstract

In research related to MIMO closed-loop feedback systems, there is much less emphasis on studying phase compared to magnitude. Additionally, in the field of system stability analysis, there is a lack of a corresponding “small phase theorem” as opposed to the famous small gain theorem. This is because defining the phase of the transfer function for MIMO systems is extremely challenging. Li QIU et al. defined sectorial phases and segmental phases for a complex matrix, and obtained a matrix small phase theorem. In this thesis, we define sectorial phases and segmental phases for a regular linear relation which are used to describe a semi-stable or stable subsystem in a MIMO LTI closed-loop feedback system. Two relation small phase theorems are obtained, which use sectorial phase and segmental phase characteristics of the regular linear relations respectively. They can use phase information to determine the stability of a MIMO system when the system contains semi-stable subsystems. The thesis also discusses the computation of segmental phases of a matrix or a regular linear relation and give a feasible algorithm. Keywords : Phase theory, small phase theorem, linear relation, stability analysis.

Date of Award	2024
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Li QIU (Supervisor)