Approximated mixed sensitivity reduction for SISO feedback systems

This paper proposes a controller synthesis method for single-input single-output (SISO) discrete-time systems by approximately minimizing an H²-normed mixed sensitivity criterion. Operating in the Discrete Fourier Transform (DFT) domain, we construct an l²-space vector minimization problem to approximate the original H² control problem. The dimension of the newly constructed problem equals to the number of the DFT points (N) chosen. The approximation in such a setting is sufficient for a reasonably small N due to the stability and short-duration characteristics of the elements involved in the problem formulation. The analytic solution of the l² problem is given, and the controller is constructed via the N Markov parameters associated with the analytic solution. Two examples are given to explain the proposed method.