On the Dependence of the Optimal H2 Performance on Sampling Rate Variability

This letter studies the attainable performance in the discrete-time
H
₂
optimization under process-independent irregular information transmission between sensor- and actuator-side parts of the controller. In particular, we are concerned with effects of the variability of the sampling rate on the attainable optimal cost. Tight upper and lower bounds on the cost are derived for fixed maximal and average sampling intervals. These bounds are shown to correspond to the maximal and minimal possible variances of sampling intervals. Further insight into the dependence of the performance on properties of the sampling sequence is provided in several special cases.