A LQG Control Problem with Degree and Robustness Constraints

In this paper, we aim to obtain the optimal LQG controller under degree and robustness constraints. This is a mixed control problem of finding the full-order controller to provide the best nominal transient performance subject to a robust stability bound. Firstly, the set of desired controllers that meet both the degree and robust stability constraints are characterized over a convex set. Then, we carry out optimization in the convex parameter set for the controller that gives optimal transient performance. Examples and observations are presented, and comparisons with other approaches show that our approach excels.