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1、IntroductiontotheMathematicalTheoryofSystemsandControlPlantControllerJanWillemPoldermanJanC.WillemsContentsPrefaceix1DynamicalSystems11.1Introduction...........................11.2Models..............................31.2.1Theuniversumandthebehavior...........31.2.2Behavioral
2、equations..................41.2.3Latentvariables....................51.3DynamicalSystems.......................81.3.1Thebasicconcept...................91.3.2Latentvariablesindynamicalsystems........101.4LinearityandTime-Invariance................151.5DynamicalBehavioralEquat
3、ions...............161.6Recapitulation.........................191.7NotesandReferences.....................201.8Exercises............................202SystemsDe?nedbyLinearDi?erentialEquations272.1Introduction...........................272.2Notation.........................
4、....282.3Constant-Coe?cientDi?erentialEquations.........312.3.1Linearconstant-coe?cientdi?erentialequations...312.3.2Weaksolutionsofdi?erentialequations.......332.4BehaviorsDe?nedbyDi?erentialEquations.........372.4.1Topologicalpropertiesofthebehavior........382.4.2Linearity
5、andtime-invariance.............432.5TheCalculusofEquations...................442.5.1Polynomialringsandpolynomialmatrices......442.5.2Equivalentrepresentations...............452.5.3Elementaryrowoperationsandunimodularpolyno-mialmatrices......................492.5.4TheBezoutid
6、entity..................522.5.5Leftandrightunimodulartransformations.....542.5.6Minimalandfullrowrankrepresentations......572.6Recapitulation.........................602.7NotesandReferences......................612.8Exercises............................612.8.1Analyticalprobl
7、ems..................632.8.2Algebraicproblems...................643TimeDomainDescriptionofLinearSystems673.1Introduction...........................673.2AutonomousSystems......................683.2.1Thescalarcase.....................713.2.2Themultivariablecase................
8、.793.3SystemsinInput/OutputForm................833.4SystemsDe?nedbyanInput/
