Fixed-order robust controller design with time-domain constraints

This paper deals with overshoot reduction in fixed order controller design for linear systems subject to polytopic uncertainty. The basis of the developed synthesis method is a recent convex parameterization for fixed-order stabilizing controllers based on the polynomial approach. Two convex constraints are developed in order to decrease the overshoot of the closed-loop step response. First, based on the existing convex parameterization and peak-to-peak gain performance a criterion is developed to minimize the peak value of the step response. In the second method, Markov parameters of the system are used to achieve a step response with less overshoot. Simulation results illustrate the effectiveness of the developed methods.