A comparison between two kinds of delay decomposition approaches to stability and stabilization for delay systems

This paper is concerned with a comparison between two stability criteria of linear time-delay systems by using different delay decomposition approaches from [4] and [7], respectively. One stability criterion is not more conservative theoretically but its numerical complexity is larger, another is not less conservative theoretically but its numerical complexity is smaller. Based on two stability criteria, the relationship of two sufficient conditions on the existence of a controller for time-delay systems are given and the numerical complexity of controller design methods by different linearization approaches are discussed. The given examples also show the relationship of these two stability criteria of linear time-delay systems.