This paper aims at presenting robustness analysis under the uncertainties of the time delay and plant parameters in symmetrically coupled dynamic systems connected through network having time delay. The delay-involved closed loop characteristic function is mathematically formulated, incorporated with active synchronization control. And the robust stability of the corresponding system is analyzed by investigating the formation of characteristic equation containing second- order terms of uncertainty variables representing delay and plant dynamics mismatches. For the two individual types of uncertainties, we elucidate details of how to compute the bounds and what they imply physically. To support the validity of the mathematical claims, numerical examples and simulations are presented.