Stability Analysis of Neural Networks

Preface
Acknowledgements
Contents
About the Authors
Acronyms
Notations
List of Figures
List of Tables
1 Introduction
	1.1 An Overview of Dynamical Systems
		1.1.1 What Is a Dynamical System?
		1.1.2 Delay Effects on Dynamical Systems
		1.1.3 Stability of Dynamical Systems
		1.1.4 Lyapunov Stability of Dynamical Systems
		1.1.5 Stability Analysis of Neural Network Models with Linear Matrix Inequality
	1.2 An Overview of Artificial Intelligence
		1.2.1 Support Vector Machine
		1.2.2 Relevance Vector Machine
		1.2.3 Genetic Programming
		1.2.4 Emotional Neural Network
		1.2.5 Least-Squares Support Vector Machine
		1.2.6 Extreme Learning Machines
		1.2.7 Minimax Probability Machine Regression
		1.2.8 Gaussian Process Regression
		1.2.9 Multivariate Adaptive Regression Spline
		1.2.10 Functional Network
	1.3 An Overview of Neural Network Models
		1.3.1 Biological Neural Networks
		1.3.2 Artificial Neural Networks
		1.3.3 Stability of Dynamical Neural Networks
	1.4 Review of Fundamental Concepts
		1.4.1 Impulsive Differential Equations
		1.4.2 Stochastic Differential Equations
		1.4.3 Markovian Jumping Systems
		1.4.4 Hopfield Neural Networks
		1.4.5 Cellular Neural Networks
		1.4.6 Bidirectional Associative Memory Neural Networks
		1.4.7 Cohen–Grossberg Neural Networks
		1.4.8 Genetic Regulatory Networks
		1.4.9 Neutral-Type Dynamical Systems
	1.5 Scope of the Book
	1.6 Organization of the Book
	References
Part I Continuous-Time Case
2 LMI-Based Stability Criteria for BAM Neural Networks
	2.1 Introduction
	2.2 Problem Statements and Mathematical Fundamentals
	2.3 Exponential Stability Criteria with Non-fragile State Estimator
	2.4 Illustrative Examples
	2.5 Summary
	References
3 Exponential Stability Criteria for Uncertain Inertial BAM Neural Networks
	3.1 Introduction
	3.2 Problem Statements and Mathematical Fundamentals
	3.3 Global Robust Exponential Stability Criteria  in the Lagrange Sense
	3.4 Illustrative Examples
	3.5 Summary
	References
4 Exponential Stability of Impulsive Cohen–Grossberg BAM Neural Networks
	4.1 Introduction
	4.2 Problem Statements and Mathematical Fundamentals
	4.3 Global Exponential Stability Criteria
	4.4 Illustrative Examples
	4.5 Summary
	References
5 Exponential Stability of Recurrent Neural Networks with Impulsive and Stochastic Effects
	5.1 Introduction
	5.2 Problem Statements and Mathematical Fundamentals
	5.3 Exponential Stability Criteria with the Fractional Delay Segments Method
	5.4 Illustrative Examples
	5.5 Summary
	References
6 Stability of Markovian Jumping Stochastic Impulsive Uncertain BAM Neural Networks
	6.1 Introduction
	6.2 Problem Statements and Mathematical Fundamentals
	6.3 Global Exponential Stability Criteria for Deterministic Models
	6.4 Global Exponentially Stability Criteria for Uncertain Models
	6.5 Illustrative Examples
	6.6 Summary
	References
7 Global Robust Exponential Stability of Stochastic Neutral-Type Neural Networks
	7.1 Introduction
	7.2 Problem Statements and Mathematical Fundamentals
	7.3 Robust Stabilization Criteria in the Mean-Square Sense
	7.4 Global Robust Exponential Stability Criteria  in the Mean-Square Sense
	7.5 Illustrative Examples
	7.6 Summary
	References
Part II Discrete-Time Case
8 Exponential Stability of Discrete-Time Cellular Uncertain BAM Neural Networks
	8.1 Introduction
	8.2 Problem Statements and Mathematical Fundamentals
	8.3 Exponentially Stability Criteria Using Halanay-Type Inequality
	8.4 Exponentially Stability Criteria for Uncertain Cases Using Halanay-Type Inequality
	8.5 Illustrative Examples
	8.6 Summary
	References
9 Exponential Stability of Discrete-Time Stochastic Impulsive BAM Neural Networks
	9.1 Introduction
	9.2 Problem Statements and Mathematical Fundamentals
	9.3 Global Exponential Stability Criteria in the Mean Square Sense
	9.4 Global Exponential Stability Criteria for Uncertain Cases in the Mean Square Sense
	9.5 Illustrative Examples
	9.6 Summary
	References
10 Stability of Discrete-Time Stochastic Quaternion-Valued Neural Networks
	10.1 Introduction
	10.2 Problem Statements and Mathematical Fundamentals
	10.3 Mean-Square Asymptotic Stability Criteria
	10.4 Illustrative Examples
	10.5 Summary
	References
11 Robust Finite-Time Passivity  of Markovian Jump Discrete-Time  BAM Neural Networks
	11.1 Introduction
	11.2 Problem Statements and Mathematical Fundamentals
	11.3 Robust Finite-Time Boundedness
	11.4 Robust Finite-Time Passivity
	11.5 Illustrative Examples
	11.6 Summary
	References
12 Robust Stability of Discrete-Time Stochastic Genetic Regulatory Networks
	12.1 Introduction
	12.2 Problem Statements and Mathematical Fundamentals
	12.3 Robustly Mean-Square Exponential Stability Criteria
	12.4 Illustrative Examples
	12.5 Summary
	References
Index