Statistical design of digital control systems

This paper is concerned with the problem of statistical design of digital control systems. A simplified design procedure is introduced. The minimum mean-square error is adopted as the performance criterion; and the system design is based upon the Wiener-Kolmogoroff theory of optimum filtering and prediction. The treatment of this optimization problem makes use of the modified -tranusform technique, and is presented in close parallel with the procedure for the statistical design of linear continuous-data control systems. By making use of some important properties of the auto-correlation sequence, the cross-correlation sequence, the pulse spectral density and the pulse cross-spectral density, the statistical design of digital control systems can be carried out in a simple and systematic manner.