Intersample variances in discrete minimum variance control

This note investigates the continuous-time response resulting from digital control of stochastic systems. A method is presented for computing the time-varying covariance between sampling instants. The results are used to examine the performance of the well-known minimum variance control strategy. It is shown that the continuous-time response is cyclo-stationary. This analysis confirms that these algorithms can have poor continuous-time responses especially for lightly damped systems. In view of these results, we suggest that it may be preferable to use alternative design procedures which give suboptimal performance at the sampling instants but which actually result in superior continuous-time results. The theoretical results in the note are substantiated by a computer simulation study.