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分数维非线性系统 建模、分析与仿真 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

分数维非线性系统 建模、分析与仿真 英文
  • （斯洛伐克）帕璀斯著 著
  • 出版社： 北京：高等教育出版社
  • ISBN：9787040315349
  • 出版时间：2011
  • 标注页数：219页
  • 文件大小：12MB
  • 文件页数：232页
  • 主题词：非线性系统(自动化) －研究－英文

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图书目录

1 Introduction1

References3

2 Fractional Calculus7

2.1 Special Functions7

2.2 Definitions of Fractional Derivatives and Integrals9

2.3 Grünwald-Letnikov Fractional Integrals and Derivatives9

2.4 Riemann-Liouville Fractional Integrals and Derivatives11

2.5 Caputo Fractional Derivatives12

2.6 Laplace Transform Method12

2.6.1 Basic Facts about the Laplace Transform12

2.6.2 Laplace Transform of Fractional Integrals14

2.6.3 Laplace Transform of Fractional Derivatives14

2.7 Fourier Transform Method15

2.7.1 Basic Facts about the Fourier Transform15

2.7.2 Fourier Transform of Fractional Integrals16

2.7.3 Fourier Transform of Fractional Derivatives17

2.8 Some Properties of Fractional Derivatives and Integrals18

2.9 Numerical Methods for Calculation of Fractional Derivatives and Integrals19

2.10 Fractional Calculus and Electricity29

2.10.1 Analogue Fractional-Order Circuits35

2.10.2 Experimental Measurement36

2.10.3 Additional Remarks37

References38

3 Fractional-Order Systems43

3.1 Fractional LTI Systems43

3.2 Fractional Nonlinear Systems47

3.3 Fractional-Order Controllers47

3.3.1 Definition of Fractional-Order Controllers47

3.3.2 Properties and Characteristics of Controller49

3.3.3 Design of Controller Parameters and Implementation51

References52

4 Stability of Fractional-Order Systems55

4.1 Preliminary Consideration55

4.2 Stability of Fractional LTI Systems63

4.3 Stability of Fractional Nonlinear Systems78

4.4 Robust Stability of Fractional-Order LTI Systems82

4.4.1 Stability Check When the Fractional Orders Are Crisp and Commensurate82

4.4.2 Stability Check When the Fractional Orders Are Also Interval Real Numbers87

4.5 Stability of Fractional-Order Nonlinear Uncertain Systems97

References98

5 Fractional-Order Chaotic Systems103

5.1 Introduction to Chaotic Dynamics103

5.2 Concept of Chua's Circuit104

5.2.1 Classical Chua's Oscillator104

5.2.2 Fractional-Order Chua's Oscillator107

5.2.3 Fractional-Order Chua-Podlubny's Oscillator113

5.2.4 Fractional-Order Chua-Hartley's Oscillator114

5.2.5 Fractional-Order Memristor-Based Chua's Oscillator114

5.3 Fractional-Order Van der Pol Oscillator127

5.4 Fractional-Order Duffing's Oscillator130

5.5 Fractional-Order Lorenz's System134

5.6 Fractional-Order Chen's System138

5.7 Fractional-Order Lü's System140

5.8 Fractional-Order Liu's System142

5.9 Fractional-Order Genesio-Tesi's System145

5.10 Fractional-Order Arneodo's System148

5.11 Fractional-Order R？ssler's System151

5.12 Fractional-Order Newton-Leipnik's System154

5.13 Fractional-Order Lotka-Volterra System160

5.14 Fractional-Order Financial System165

5.15 Fractional-Order CNN168

5.16 Fractional-Order Volta's System171

References181

6 Control of Fractional-Order Chaotic Systems185

6.1 Preliminary Considerations185

6.2 A Survey of Control Strategies187

6.3 Examples:Feed-Back Control of Chaotic Systems188

6.3.1 Sampled-DataControl of Chua's Oscillator188

6.3.2 Sliding Mode Control of the Economical System192

References197

7 Conclusion201

References203

Appendix A A List of Matlab Functions207

Appendix B Laplace and Inverse Laplace Transforms211

Glossary215

Index217

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