Mixed H²-norm sensitivity minimization in the DFT domain for control system design

In this paper, we deal with the problem of designing a feedback controller for linear time-invariant discrete-time systems that minimizes the H²-norm of a mixed sensitivity criterion. Operating in the Discrete Fourier Transform (DFT) domain, we construct an l²-space vector minimization problem that can be made arbitrarily close to the original H² problem if the size of the DFT becomes large. The advantage of using the proposed method is that the solution in the l²-space can be analytically expressed, and it can be efficiently calculated via multichannel algorithms due to the particular structure of the matrices in the DFT domain. Thus, the computational complexity of the approach introduced is small despite the relatively larger dimension of the matrices involved. The method is demonstrated through examples.