A Mixed H2/H∞ Control Problem with Controller Degree Constraint

In this paper, we consider a special mixed H₂/H_∞ optimal control problem which is to obtain the optimal H₂ controller under H_∞ norm and controller degree constraints for an SISO plant. The H_∞ norm constraint on the controller is to achieve a certain level of closed-loop stability robustness against the gap metric, nu-gap metric, or normalized coprime factor uncertainties. The degree constraint requires the degree of the controller to be bounded by that of the plant. We first characterize the set of all feasible stabilizing controllers that meet both the degree and H_∞ norm constraints in terms of a finite dimensional convex set. We then carry out an optimization over the convex parameter set to find the controller that gives the optimal H₂ transient performance. Examples and observations are presented, and comparisons with the results obtained by other H₂/H_∞ mixed optimization methods are made