On the order of stable compensators for a class of time-delay system

The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that the compensator’s order will go up. This note considered the order of stable compensators for a class of time-delay systems. First, it is shown that for single-loop plants with at most one real right-half plane zero, a special upper bound for the minimal order of a strongly stabilizing compensator can be obtained in terms of the plant order; Second, it is shown that approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeroes are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator.