Controller design via Pade approximation can lead to instability

The Pade approximation is often used to approximate a pure time delay by a rational transfer function. In this paper, we show via examples that PID controllers that stabilize such an approximation may actually be destabilizing for the true system. Recent results, giving the entire set of stabilizing PID controllers for finite dimensional linear time invariant systems as well as for systems with time delay, are used to make a comparative study, through examples, of the stabilizing sets for the true plant and its Pade approximants