Robust controller design: mixed H² performance optimization for linear discrete-time systems

The feedback controller design for linear time-invariant discrete-time systems via minimizing the H²-norm of a mixed sensitivity criterion is revisited. By borrowing some of the techniques from signal/image processing, a new approach is presented to tackle the H² control problem. Operating in the Discrete Fourier Transform (DFT) domain, we construct a minimization problem in the l²-space to approximate the original H² problem. The approximation in such a setting is sufficient for a reasonably small number of DFT-point chosen due to the stability and short-duration characteristics of the matrix elements involved in the design problem. Via the partially block circular structure of the matrices involved in the DFT domain, the l² vector-optimization problem can be efficiently solved through matrix algebraic techniques.