Approximation of neutral delay-differential equations

[Mathematical notation cannot be correctly represented here; please see PDF below for full equations.] We study questions related to stability and approximation of the system of linear neutral delay differential equations [equation] with appropriate initial data. Here [A, B subscript 1, B subscript 2,..., B subscript n and C subscript 1, C subscript 2,..., C subscript n] are complex [m x m] matrices for a natural number [m] and [r subscript 1, r subscript 2,... r subscript n] are positive numbers. We construct a new delay-independent sufficient condition for exponential stability of the solution semigroup associated with this equation. We obtain our condition by using the idea of renorming the state space to obtain a strong dissipative inequality on the generator of the solution semigroup. We also construct a new semidiscrete approximation scheme which yields convergence for both the solution semigroup and its adjoint. Finally, we discuss several examples to compare our results with existing results in the literature