Matrix and Polynomial Approach to Dynamic Control Systems

Preface
SymbolList
Chapter1SwapMatrixandLeftSemi-tensorProduct
1.1Multi-dimensionalData
1.2SwapMatrix
1.3LeftSemi-tensorProductofMatrices
1.4WhySemi-tensorProduct
Chapter2PropertiesofSemi-TensorProduct
2.1LinearMappingonMatrices
2.2PropertiesofLeftSemi-tensorProduct
2.3LeftSemi-tensorAlgebra
2.4RightSemi-tensorProduct
2.5Semi-tensorProductofGeneralMatrices
Chapter3TensorFormofPolynomials
3.1TensorExpressionofPolynomials
3.2DifferentialForms
3.3BasisTransformations
3.4TaylorExpansionofMulti-dimensionalMappings
Chapter4SomeApplications
4.1StructureofanAlgebra
4.2LieDerivative
4.3Connection
4.4CarlemanLinearization
4.5FormulationonMorgen'sProblem
4.6NumericalMethodofMorgen'sProblem
Chapter5TensorAlgebra
5.1PermutationMatrix
5.2TensorAlgebra
5.3Pseudo-exteriorDerivative
Chapter6LyapunovMapping
6.1TheSpectrumofLA
6.2NormandRepresentationofLAH
6.3CommonLyapunovFunctionsforTwoMatrices
6.4ACommonLyapunovFunctionforaSetofMatrices
6.5AnAlgorithm
Chapter7LinearSymmetry
7.1SymmetryofDynamicSystems
7.2SymmetryviaLie-groupApproach
7.3SymmetryviaLie-algebraApproach
7.4SymmetryUnderRotation
7.5SymmetryofPlanarSystems
7.6LargestInvariantGroup
Chapter8NormalFormRepresentationofControlSystems
8.1NormalForm
8.2StructureAnalysis
8.3LinearApproximationofNon-linearSystems
8.4SystemofBallandBeam
Chapter9ControlRouthArrayandItsApplications
9.1RouthArrayCriterion
9.2ControlRouthArray
9.3SolvingRouthPolynomialInequalities
9.4StateorOutputFeedbackStabilization
9.5StabilityofIntervalMatrices
Chapter10HamiltonianRealizations
10.1Pseudo-HamiltonianSystem
10.2HamiltonianRealization
10.3ApproximateHamiltonianRealizations
10.4StabilizationviaHamiltonianRealization
Chapter11StabilizationviaDesignedCenterManifold
11.1CenterManifoldApproachtoStabilization
11.2LyapunovFunctionwithHomogeneousDerivative
11.3SomeSufficientConditionsforNegativity
11.4StabilizationofSystemswithZeroCenter
11.5StabilizationforOddInjectionDegreeCenter
11.6StabilizationforEvenInjectionDegreeCenter
11.7StabilizationforMixedInjectionDegreeCenter
Chapter12StabilizationofSystemswithVariousCenter
12.1GeneralizedLFHD
12.2Stabilizationof2-zeroCenterDynamics
12.3StabilizationofSystemswithOscillatoryCenter
Bibliography
Index