矩阵不等式约束下的矩阵逼近及鲁棒控制中的应用

？Thispaperdealswithageneralclassofoptimizationproblemsinrobustcontrolwithgivenexpectationvalueofperformanceindex,whichcanbetransformedintotheproblemofmatrixapproximationwithmatrixinequalitiesconstraints.Theoremforexistenceandtheuniquenessofthesolutionsofmatrixapproximationwithlinearmatrixinequalities(LMIs)constraintsispresentedandalgorithmsforsolvingtheproblemsofmatrixapproximationwithmatrixinequalitiesconstraintsaregivenbasedonthefactthatsuchproblemscanbeconvertedintothegeneralizedeigenvalueproblem(GEVP)ofLMI.Examplesaregiventoillustratethemainresultsofthepaper.