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Tables of Contents for Nonlinear Noninteger Order Systems
Chapter/Section Title
Page #
Page Count
Preface
1
2
Non Integer Order Circuits and Systems
3
12
Introduction: Non Integer Order Physical Laws
3
1
Non Inductive Transmission Line
4
1
1/f Noise Spectra
5
2
Polarization Phenomena
7
1
Diffusion Phenomena
8
1
Acoustic Phenomena
9
2
Frequency Modulation and Bessel Function of the First Kind
11
4
Main Results on Non Integer Order Systems
15
40
Non Integer Integration: Historical Notes
15
1
Preliminaries and Definitions
16
1
Laplace Transforms and System's Representation
17
3
General Properties of Fractional Systems
20
5
Impulse Response of a General Fractional System
25
3
Numerical Differintegration
28
3
Approximation of Non Integer Order Systems via Integer Order Systems
Infinite Order and Non Integer Order
31
1
Frequency Domain Approximation
32
3
Inverse Method: Non Integer Order Modeling
35
6
An Example of Time Domain Approximation
41
5
Genetic Algorithms to Approximate Non Integer Order System
46
9
Response Approximation
46
4
Genetic Algorithms (GAs)
50
3
Self Similarity
53
2
Control Problem: Non Integer Order Feedback Controllers
55
46
Control Design: a Brief Review
56
2
Non Integer Order Correction
58
4
The CRONE Control
62
2
Complex Integration and Evolution of the CRONE
64
3
Non Integer Derivative Control of the Steady State in Chua's Circuit
67
17
β Parameter and Piecewise Linear Resistor
70
7
From Integer to Fractional PD Control of Chua's Circuit
77
7
PIλDμ Non Integer Order Controller
84
11
Non Linear System Control via PIλDμ Controller
95
6
Non Integer Order Cellular Neural Network Systems
101
24
Standard and Non Integer Order CNNs
101
4
From Integer to Non Integer Order CNNs
104
1
Image Processing Applications
105
10
Autowaves in Non Integer Order CNNs
115
10
The Non Integer Order CNN Simulator
117
1
Simulation of the Complex Phenomena
117
8
Circuit Design of Non Integer Order Chaotic Systems
125
22
Non Integer Order and Chaos
125
1
The Duffing System
126
6
Non Integer Order CNNs and Chaos
132
9
Numerical Example
140
1
The Two-cell CNN Circuit
141
6
Conclusion
147
4
The Status of the Non Integer Order System Research
147
1
What it Needs to be Done
148
1
Scheme of the Book
149
2
References
151
8
Appendix
159
40
Matlab Function for Integration
159
4
Matlab Function for the Study of Non Integer Order Systems
163
1
Matlab Function for the Realization of the Singularity Function Method
164
1
Description of the Simulator of the Non Integer Order CNN (QCNNSim)
164
30
Non Integer Order Plant and PD Controller
194
5
Index
199