A discrete time optimal control for linear time-delay systems is devel
oped to ensure that all closed-loop eigenvalues will lie inside a circ
ular region centred at (beta, 0) with radius alpha. It is shown that b
y suitable manipulations the problem can be reduced to a standard disc
rete time quadratic regulator problem. An illustrative example is incl
uded to demonstrate the applicability of the proposed method.