On feedback stabilization of neutral time delay systems with infinitely many unstable poles

It is shown that strictly proper neutral time delay systems having at least one asymptotic pole chain converging to a vertical line Re(s) = σ > 0 cannot be stabilized by a proper controller. A special coprime factorization can be obtained for such systems with infinitely many unstable poles, provided they are bi-proper (i.e. proper, but not strictly proper). From this factorization, stabilizing feedback controllers are obtained. Necessarily, all stabilizing controllers for this type of plants are also bi-proper.