introduction to mathematical systems theory - a behavioral approach, willems polderman (springer, 1998)

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1、ThisispagexxvPrinter:OpaquethisContentsSeriesPrefacevPrefaceviiAcknowledgementsxxiHowtousethisBookxxiii1DynamicalSystems11.1Introduction.............................11.2Models...............................31.2.1Theuniversumandthebehavior..............31.2.2Behavioralequations....

2、................31.2.3Latentvariables.......................51.3DynamicalSystems.........................81.3.1Thebasicconcept......................81.3.2Latentvariablesindynamicalsystems...........101.4LinearityandTime-Invariance...................151.5DynamicalBehavioralEquation

3、s..................161.6Recapitulation............................18xxviContents1.7NotesandReferences.......................191.8Exercises..............................192SystemsDefinedbyLinearDifferentialEquations272.1Introduction.............................272.2Notation.........

4、......................282.3Constant-CoefficientDifferentialEquations............312.3.1Linearconstant-coefficientdifferentialequations.....312.3.2Weaksolutionsofdifferentialequations..........332.4BehaviorsDefinedbyDifferentialEquations............372.4.1Topologicalpropertiesofthebeh

5、avior...........372.4.2Linearityandtime-invariance...............422.5TheCalculusofEquations.....................432.5.1Polynomialringsandpolynomialmatrices........432.5.2Equivalentrepresentations.................442.5.3Elementaryrowoperationsandunimodularpolynomialmatrices.......

6、....................482.5.4TheBezoutidentity.....................512.5.5Leftandrightunimodulartransformations.........532.5.6Minimalandfullrowrankrepresentations.........552.6Recapitulation............................582.7NotesandReferences........................592.8Exercises...

7、...........................592.8.1Analyticalproblems....................612.8.2Algebraicproblems.....................623TimeDomainDescriptionofLinearSystems653.1Introduction.............................653.2AutonomousSystems........................663.2.1Thescalarcase.............

8、..........683.2.2Themultivariable