This book discusses recent research on the stability of various neural networks with constrained signals. It investigates stability problems for delayed dynamical systems where the main purpose of the research is to reduce the conservativeness of the stability criteria. The book mainly focuses on the qualitative stability analysis of continuous-time as well as discrete-time neural networks with delays by presenting the theoretical development and real-life applications in these research areas. The discussed stability concept is in the sense of Lyapunov, and, naturally, the proof method is based on the Lyapunov stability theory. The present book will serve as a guide to enable the reader in pursuing the study of further topics in greater depth and is a valuable reference for young researcher and scientists.
Author(s): Grienggrai Rajchakit, Praveen Agarwal, Sriraman Ramalingam
Publisher: Springer
Year: 2021
Language: English
Pages: 430
City: Singapore
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
