Rationalization of singularly perturbed continuous systems with time delays

The state equation of a continuous time system with time delay is nonlinear. Therefore, its transfer function is irrational, which is difficult to solve. However, the transfer function of a discrete time state equation with time delay is rational. Hence, the problem can be solved easily. A rationalization of the singularly perturbed continuous system of single and multiple time delays is presented by setting a delay coefficient. The technique is a powerful tool when solving the singularly perturbed continuous equation with single and multiple time delays instead of when using numerical methods such as the Runge-Kutta algorithm.