Multiobjective H2/H∞ control

For a linear time-invariant system with several disturbance inputs and controlled outputs, we show how to minimize the nominal H₂-norm performance in one channel while keeping bounds on the H₂-norm or H_∞-norm performance (implying robust stability) in the other channels. This multiobjective H₂ /H_∞-problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems. We show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller. If it exists, we reveal how the novel trick of optimizing the trace norm of the Youla parameter over certain convex constraints allows one to design a nearly optimal controller whose Youla parameter is of the same order as the optimal one