Dead-beat control with robustness

A design procedure for dead-beat control systems with robustness is proposed for general unstable non-minimum-phase plants. Characterization of dead-beat controllers is given in terms of closed-loop error response, based on the YJB parameterization of all stabilizing controllers. The optimally robust design is formulated in terms of a robustness index that is essentially the same as the L2-norm of sensitivity. For a given number of dead-beat steps, a procedure for computing the optimally robust dead-beat controller is derived. The limit value of the robustness index as the number of dead-beat steps goes to infinity is also given. Some numerical examples are shown to illustrate the theoretical results.