Robustness analysis for parameter matrices of global exponential stability time varying delay systems

This paper analyzes the robustness of global exponential stability time varying delay systems subjected to parameter uncertainty. Given a globally exponentially stable time varying delay systems, the problem to be addressed herein is how much parameter uncertainty the systems can withstand to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the systems to sustain global exponential stability. Moreover, we prove theoretically that, for globally exponentially stable systems, if additive parameter uncertainty is smaller than the derived upper bounds arrived at here, then the perturbed systems are guaranteed to also be globally exponentially stable. A numerical example is provided to illustrate the theoretical result.