Comparison principle for positive time-delay systems: An extension and its application

Abstract

This paper proposes an extended comparison principle for continuous-time linear positive time-delay systems. Unlike the existing comparison principle, which uses a constant initial function for the comparison system, instead, we propose a time-varying initial function in order to derive a more general solution comparison. Based on this extended comparison principle, we develop a novel computational method, which exploits more effectively the information of the initial value function, to derive tighter exponential estimates for the state vector of positive time-delay systems. The effectiveness of our developed method is illustrated through two numerical examples.