This book mainly introduces some new design methods and ideas about fractional-order nonlinear systems, the main contents include: exponential stability analysis and adaptive projective synchronization for fractional-order T-S fuzzy neural networks； projective synchronization for two identical and nonidentical time-delayed fractional-order T-S fuzzy neural networks； mixed H∞/passive projective synchronization for fractional-order neural networks and fractional-order memristor-based neural networks； H∞ tracking control and adaptive interval type-2 fuzzy sliding mode control for fractional-order nonlinear systems.
This book is suitable for professional researchers in the fields of control science and engineering, industrial automation, electrical automation and mechanical engineering, but also can be used as a reference material for relevant science and technical engineers.
Table of Contents
Preface
Chapter 1 Introduction
1．1 Brief historical ovder lew
1．1．1 Fractional order systems
1．1．2 Fractionru order neural works
1．1．3 T-S fuzzy systems
1．1．4 Synchronization
1．1．5 Adaptive control
1．1 6 Sliding mode control
1．1．7 Tacking control
1．1．8 Type-2 fuZzy control
1．1．9 H∞， Ipassive performance
1．2 Why fractional order
1．3 Organization of the book．
References
Chapter 2 Fundamentals of fractiona1-order system8
2．1 Several important fimctions of fractional calculus
2．2 Fractional integral and derivatives
2．3 Some important lemmas
References
Chapter 3 Exponential stability analysis of fractiona1-order T-S PlZzy neural works
3．1 Problem statement
3．2 Stability esal ySlS
3．3 Numerical Examples
3．4 Conclusions
References
Chapter 4 Adaptive projective synchronization for fractional-order T-S fuzzy neural works．
4．1 Problem statement
4．2 Synchronization controller design and analysis
4．2．1 Controller desJ．gn
4．2．2 Stability analyse
4．3 Numerical simulation
4．3．1 Numerical example
4．3．2 Application to secure munications
4．4 Conclusions
References
Chapter 5 Projective synchronization for two nonidentical timeesdelayed fractional-order T-S fuzzy neural works
5．1 Problemstatement
5．2 Synchronization controller design and analysis
5．2．1 Sliding mode controller design
5．2．2 Stability analysis
5．3 Numerical simu1ation
5．4 Conclusions
R．eferences
Chapter 7 Mixed H∞， /passive projective synchronization for fractional-order neural works
7．1 Problemstatement
7．2 Synchronization controller design and analysis
7．2．1 Adaptive controller design
7．2．2 Perlormance analysis
7．3 Nnmerical simulation
7．3．1 Numerical simulation： Case 1
7．3．2 Application to secure muniex止ions
7．3．3 Numericalsimulation： Case 2
7．4 Conclusions
References
Chapter 8 Mixed H∞， /passive projective synchronization for nonidentical uncertain fractional-order neural works
8．1 Problem statement
8．2 Sliding mode controller design and analysis
8．2．1 Sliding mode controller design
8．2．2 Stability analysis
8．3 Numerical Simulation
8．4 Conclusions
References
Chapter 9 Mixed H∞， md passive projective synchronization for fractional-order memristor-based neural works
9．1 Problemstatement
9．2 Synchronization controller design and analysis
9．2．1 Controller design
9．2．2 Stability analysis
9．3 Numerical simulation
9．3．1 Three-dimension memristor-based fractional-order neural works
9．3．2 Thr dimension fractional-order Hopfield neural works
9．4 Conclusions
References
Chapter 10 Adaptive sliding mode projective synchronization for fractional-order memristor-based neural works
10．1 problemstatement
10．2 Main Results
10．3 Num，erical simulation
10．3．1 Three dimeeslon memristor-based fractional-order neural workswith time-varying delays
10．3．2 Thr．，．←dimeeslon fractional-ordesHopfield neural works withfixed thne delays
10．4 Conclusions
References
Chapter 11 H∞， tracking control for nonlinear fractional-order systems via output feedback design
11．1 Problem Statement
11．2 Main results
11．2．1 Stability analysis
11．2．2 Controller design
11．3 Numerical Example
11．4 Conclsesese
Chapter 12 Adaptive interval typ-2 fuzzy sliding mode control for fractional-order nonlinear systems
12．1 Interval typE？ 2 fuzzy logic system
12．2 Main result
12．2．1 Controller design
12．2．2 Finite time stability analysis
12．3 Num．erical example
12．3．1 Application to fractional-order Lorenz chestic system
12．3．2 Application to a chestic non-autonomoeselectromechmical transducer model
12．3．3 Comparison example
12．4 Concles10ns
References
