Stability analysis and optimal control of stochastic

OptimLett(2014)8:1905–1920DOI10.1007/s11590-013-0687-5ORIGINALPAPERStabilityanalysisandoptimalcontrolofstochasticsingularsystemsQinglingZhang·ShuangyunXingReceived:26January2013/Accepted:25August2013/Publishedonline:27September2013©Springer-VerlagBerlinHeidelberg2013AbstractInthispaper,problemsofstabilityandoptimalcontrolforaclassofsto-chasticsingularsystemsarestudied.Firstly,undersomeappropriateassumptions,somenewresultsaboutmean-squareadmissibilityaredevelopedandthecorrespond-ingLMIsufficientconditionisgiven.Secondly,finite-timehorizonandinfinite-timehorizonlinearquadratic(LQ)controlproblemsforthestochasticsingularsystemareinvestigated,inwhichthecoefficientsareallowedtoberandomincontrolinputandquadraticcriterion.SomeresultsinvolvingnewstochasticgeneralizedRiccatiequationarediscussedaswell.Finally,theproposedLQcontrolmodelforstochasticsingularsystemsprovidesanappropriateandeffectiveframeworktostudytheport-folioselectionprobleminlightoftherecentdevelopmentongeneralstochasticLQproblems.KeywordsStochasticsingularsystems·Mean-squarestability·Linearquadraticcontrol·StochasticgeneralizedRiccatiequation1IntroductionSingularsystems,alsoknownasdescriptorsystems,generalizedstate-spacesystemsandimplicitsystems,aredescribedbydifferential-algebraicequations(DAEs).Sin-gularsystemshavebeenextensivelystudiedoverthepastdecadesduetothefactthattheycandescribeagreatmanynaturalphenomenainphysicalsystemssuchasQ.Zhang(B)·S.XingInstituteofSystemsScience,NortheasternUniversity,Shenyang110189,Liaoning,C