Stability analysis of multiple time-delay systems with applications to supply chain management

Abstract

Time-Delay Systems (TDS) arise in many applications from diverse areas such as economy, biology, population dynamics, traffic flow and communication systems. Asymptotic stability analysis of even linear time-invariant time-delay systems is a notoriously complex task due to the NP-hard nature of the stability problem. Additionally, consideration of multiple delays totally hampers the existing stability analyses which are limited to less than three delays. There is still no comprehensive treatment for the most general time-delay systems where the system order, the number of delays or the rank conditions of the system matrices are not limited. All the existing techniques are case-specific and derived only for lower order time-delay systems. The main goal of this dissertation is to develop a stability analysis procedure for the most general linear time-invariant multiple time-delay systems, relaxing all the mentioned limitations.