New approach to the mixed H²-norm sensitivity minimization

The robust controller design based on the minimization of the H²-norm of a mixed sensitivity function is considered. Two weighting functions and a weighting factor are introduced in the control design to trade off between feedback properties in different frequency ranges. By working in the DFT domain, we convert the original H²-norm minimization problem into a problem of solving a vector minimization in the l²-space. The advantage of using this approach is that its solution can be analytically expressed and numerically calculated via existing algorithms. The optimal estimate can be efficiently computed due to the particular block structure of the matrices involved. The approximation can be made arbitrarily close to the original H² minimization problem if the number of the DFT points is large. Two examples are also given to demonstrate the effectiveness of our approach.