A discrete Fourier transform approach to a constrained mixed H² sensitivity optimization with applications

This paper addresses a robust controller design for multiinput-multioutput (MIMO) discrete-time systems by approximately solving a constrained mixed H² sensitivity minimization problem. Using some of the digital image restoration techniques and by working in the discrete Fourier transform (DFT) domain, we convert the H² control problem into a constrained vector minimization problem in the ℓ²-space. A two-stage solution approach is detailed and the robust controller is constructed. The advantage of using the proposed method is that the ℓ²-space solution can be analytically expressed and efficiently calculated via existing multichannel algorithms due to the partially block circular structure of the matrices involved in the DFT domain. The approximation can be made arbitrarily close to the original H² control problem if the number of the DFT points is large. Several examples are given to demonstrate the feasibility of the proposed method.