Robustness of the Smith predictor with respect to uncertainty in the time-delay parameter

The robust stability of the Smith predictor scheme for time-delay compensation is analyzed with respect to uncertainty in the time-delay parameter. Appropriate definitions are introduced for the phase margin and complementary phase margin of nonminimum-phase systems, and are used to characterize the domains of stability for the closed loop using a Nyquist approach. Rigorous arguments are used to show that the stability domain is discontinuous when the nominal Nyquist function has more than one magnitude-crossover points. Robust stability results are given for the cases where the Nyquist plot has no magnitude-crossover points, and when it has a single or multiple crossover points. The results are illustrated through an example.