Robust performance of discrete-time linear systems under partial statistical information for exogenous signals

Performance under partial statistical information refers to the problem of minimizing the worst case variance of the regulated output over the class of exogenous signals whose autocorrelation function is partially specified. We consider this problem in the presence of linear time-invariant uncertainty. A sufficient frequency dependent LMI condition is derived for robust analysis. This condition is equivalent to the robust ℋ₂ results of Paganini (1999) obtained by set-based white noise modeling. In addition to providing a new interpretation, our result can be seen as a bridge between robust ℋ ₂ and ℋ_∞. problems