Quantitative robustness measure of uncertain time delay systems via nonsingularity analysis

The objective of this paper is to derive an upper bound for the delay time constant such that a linear uncertain time delay system still keeps its asymptotic stability, if it is nominally stable and the delay time constant remains smaller than the upper bound. The problem is solved by using matrix measure and nonsingularity analysis of matrices, and the results are shown to be less conservative than previous results.