ROBUST, FRAGILE, OR OPTIMAL

In this paper, we show by examples that optimum and robust controllers , designed by using the H-2, H-infinity, l(1), and mu formulations, ca n produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller de stabilize the closed-loop control system. The examples show that this fragility usually manifests itself as extremely poor gain and phase ma rgins of the closed-loop system. The calculations given here should ra ise a cautionary note and draw attention to the larger issue of contro ller sensitivity which may be important in other nonoptimal design tec hniques as well.