On the numerical approximations for linear functional differential equations with input and output delays

In this paper we state some new results on the approximations for linear retarded functional differential equations with delays in control and observation. We consider the finite difference (i.e., averaging) approximation scheme for such systems treated as evolution equations in the state space setup, and we establish several basic properties of the approximation scheme. These results are extensions of recent results of Lasiecka and ManitiusL1 to the case of systems with input and output delays.