Constrained optimal synthesis and robustness analysis by randomized algorithms

We extend the existing order statistics distribution theory to the general case in which the order statistics is associated with certain constraints and the distribution of population is not assumed to be absolutely continuous. In particular, we derive an inequality on distribution for related order statistics. Moreover, we also propose two different approaches in searching reliable solutions to the robust analysis and optimal synthesis problems under constraints. Furthermore, minimum computational effort is investigated and bounds for sample size are derived