Constrained robustness analysis by randomized algorithms

This paper shows that many robust control problems can be formulated as con strained optimization problems and can be tackled by using randomized algor ithms. Two different approaches in searching reliable solutions to robustne ss analysis problems under constraints are proposed, and the minimum comput ational efforts for achieving certain reliability and accuracy are investig ated and bounds for sample size are derived. Moreover, the existing order s tatistics distribution theory is extended to the general case in which the distribution of population is not assumed to be continuous and the order st atistics is associated with certain constraints.