Optimal tracking with fixed order controllers

For discrete-time scalar systems, we propose an approach for designing feedback controllers of fixed order to minimize an upper bound on the peak magnitude of the tracking error to a given command input. The work makes use of linear programming to design over a class of closed-loop systems proposed for the rejection of non-zero initial conditions and bounded disturbances. Performance robustness in the form of a guaranteed upper bound on the peak magnitude of the tracking error under plant uncertainty is incorporated into the formulation.