Linear Matrix Inequalities in Control-2004-Ca

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1、LinearMatrixInequalitiesinControlCarstenSchererandSiepWeilandDelftCenterforSystemsandControlDepartmentofElectricalEngineeringDelftUniversityofTechnologyEindhovenUniversityofTechnologyTheNetherlandsTheNetherlandsContentsPrefacevii1Convexoptimizationandlinearmatrixin

2、equalities11.1Introduction.......................................11.2Factsfromconvexanalysis...............................21.3Convexoptimization..................................71.3.1Localandglobalminima............................71.3.2Uniformbounds.............

3、...................81.3.3Dualityandconvexprograms.........................91.3.4Subgradients..................................121.4Linearmatrixinequalities................................151.4.1Whatarethey?.................................151.4.2Whyaretheyinteresti

4、ng?...........................171.4.3Whataretheygoodfor?............................191.4.4Howaretheysolved?..............................231.4.5WhataredualLMIproblems?.........................261.4.6Whenweretheyinvented?...........................271.5Furtherreadi

5、ng.....................................29iiiCONTENTS1.6Exercises........................................292Dissipativedynamicalsystems332.1Introduction.......................................332.2Dissipativedynamicalsystems.............................342.2.1Definiti

6、onsandexamples............................342.2.2Aclassificationofstoragefunctions......................372.2.3Dissipationfunctions..............................392.3Lineardissipativesystemswithquadraticsupplyrates.................392.3.1Mainresults.................

7、..................402.3.2Dissipationfunctionsandspectralfactors...................432.3.3TheKalman-Yakubovich-Popovlemma....................452.3.4Thepositivereallemma............................472.3.5Theboundedreallemma............................472.4Interconnec

8、teddissipativesystems...........................482.5Furtherreading.....................................502.6Exercises...........................