分数维非线性系统 : 建模、分析与仿真

Introduction

References

2 Fractional Calculus

2.1 Special Functions

2.2 Definitions of Fractional Derivatives and Integrals

2.3 Grtinwald-Letnikov Fractional Integrals and Derivatives

2.4 Riemann-Liouville Fractional Integrals and Derivatives

2.5 Caputo Fractional Derivatives

2.6 Laplace Transform Method

2.6.1 Basic Facts about the Laplace Transform

2.6.2 Laplace Transform of Fractional Integrals

2.6.3 Laplace Transform of Fractional Derivatives

2.7 Fourier Transform Method

2.7.1 Basic Facts about the Fourier Transform

2.7.2 Fourier Transform of Fractional Integrals

2.7.3 Fourier Transform of Fractional Derivatives

2.8 Some Properties of Fractional Derivatives and Integrals

2.9 Numerical Methods for Calculation of Fractional Derivatives and Integrals

2.10 Fractional Calculus and Electricity

2.10.1 Analogue Fractional-Order Circuits

2.10.2 Experimental Measurement

2.10.3 Additional Remarks

References

3 Fractional-Order Systems

3.1 Fractional LTI Systems

3.2 Fractional Nonlinear Systems

3.3 Fractional-Order Controllers

3.3.1 Definition of Fractional-Order Controllers

3.3.2 Properties and Characteristics of Controller

3.3.3 Design of Controller Parameters and Implementation

References

4 Stability of Fractional-Order Systems

4.1 Preliminary Consideration

4.2 Stability of Fractional LTI Systems ：

4.3 Stability of Fractional Nonlinear Systems

4.4 Robust Stability of Fractional-Order LTI Systems

4.4.1 Stability Check When the Fractional Orders Are Crisp and Commensurate

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

4.5 Stability of Fractional-Order Nonlinear Uncertain Systems

References

5 Fractional-Order Chaotic Systems

5.1 Introduction to Chaotic Dynamics

5.2 Concept of Chuas Circuit

5.2.1 Classical Chuas Oscillator

5.2.2 Fractional-Order Chuas Oscillator

5.2.3 Fractional-Order Chua-Podlubnys Oscillator

5.2.4 Fractional-Order Chua-Hartleys Oscillator

5.2.5 Fractional-Order Memristor-Based Chuas Oscillator

5.3 Fractional-Order Van der Pol Oscillator

5.4 Fractional-Order Duffings Oscillator

5.5 Fractional-Order Lorenzs System

5.6 Fractional-Order Chens System

5.7 Fractional-Order Ltis System

5.8 Fractional-Order Lius System

5.9 Fractional-Order Genesio-Tesis System

5.10 Fractional-Order Arneodos System

5.11 Fractional-Order R6sslers System

5.12 Fractional-Order Newton-Leipniks System

5.13 Fractional-Order Lotka-Volterra System

5.14 Fractional-Order Financial System

5.15 Fractional-Order CNN

5.16 Fractional-Order Voltas System

References

6 Control of Fractional-Order Chaotic Systems

6.1 Preliminary Considerations

6.2 A Survey of Control Strategies

6.3 Examples： Feed-Back Control of Chaotic Systems

6.3.1 Sampled-Data Control of Chuas Oscillator

6.3.2 Sliding Mode Control of the Economical System

References

7 Conclusion

References

Appendix A A List of Matlab Functions

Appendix B Laplace and Inverse Laplace Transforms

Glossary

Index

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