State-space solutions to Hadamard weighted ℋ∞and ℋ2control problems

Variations of the standard H∞ and H 2 control problems are presented. State-space solutions are given for the problems of weighting the individual elements of a closed loop transfer function while (i) satisfying an H∞-Frobenius norm bound or (ii) minimizing the H 2 norm of the closed loop. The optimal H∞-Frobenius case is analysed and it is shown that the optimal controller is often unique, in contrast to the standard H∞ control problem. The solutions of an algebraic Riccati equation are examined in the H 2 case to reveal the structure of the H 2 optimal controller