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

• We investigate the robust stability for the stable system.
• We only need the coefficients of global exponential stability.
• If additive uncertainty is smaller than the results here, the system is also stable.
• We prove the robust stability from theoretically.

In this paper, we analyze the robustness of global exponential stable stochastic delayed systems subject to the uncertainty in parameter matrices. Given a globally exponentially stable systems, the problem to be addressed here is how much uncertainty in parameter matrices the systems can withstand to be globally exponentially stable. The upper bounds of the parameter uncertainty intensity are characterized by using transcendental equation for the systems to sustain global exponential stability. Moreover, we prove theoretically that, the globally exponentially stable systems, if additive uncertainties in parameter matrices are smaller than the upper bounds arrived at here, then the perturbed systems are guaranteed to also be globally exponentially stable. Two numerical examples are provided here to illustrate the theoretical results.