Qualitative Analysis and Contr

This book focuses on the stability of the dynamical neural system， synchronization of the coupling neural system and their applications in automation control and electrical engineering. The redefined concept of stability， synchronization and consensus are adopted to provide a better explanation of the complex neural network. Researchers in the fields of dynamical systems， computer science， electrical engineering and mathematics will benefit from the discussions on complex systems. The book will also help readers to better understand the theory behind the control technique and its design.

1 Introduction to Neural Networks
1.1 Natural and Artificial Neural Networks
1.2 Models of Computation
1.3 Networks of Neurons
1.4 Associative Memory Networks
1.5 Hopfield Neural Networks
1.6 Cohen-Grossberg Neural Networks
1.7 Property of Neural Network
1.8 Information Processing Capacity of Dynamical Systems
1.9 Stability of Dynamical Neural Networks
1.10 Delay Effects on Dynamical Neural Networks
1.11 Features of LMI-Based Stability Results
1.12 Summary
References

2 Prelinunaries on Dynamical Systems and Stability Theory
2.1 Overview of Dynamical Systems
2.2 Definition of Dynamical System and Its Qualitative Analysis
2.3 Lyapunov Stability of Dynamical Systems
2.4 Stability Theory
2.5 Applications of Dynamical Systems Theory
2.6 Notations and Discussions on Some Stability Problems
2.6.1 Notations and Preliminaries
2.6.2 Discussions on Some Stability Definitions
2.7 Summary
References

3 Survey of Dynamics of Cohen-Grossberg-Type RNNs
3.1 Introduction
3.2 Main Research Directions of Stability of RNNs
3.2.1 Development of Neuronal Activation Functions
3.2.2 Evolution of Uncertainties in Interconnection Matrix
3.2.3 Evolution of Time Delays
3.2.4 Relations Between Equilibrium and Activation Functions
3.2.5 Different Construction Methods of Lyapunov Functions
3.2.6 Expression Forms of Stability Criteria
3.2.7 Domain of Attraction
3.2.8 Different Kinds of Neural Network Models
3.3 Stability Analysis for Cohen-Grossberg-Type RNNs
3.3.1 Stability on Hopfield-Type RNNs
3.3.2 Stability on Cohen-Grossberg-Type RNNs
3.3.3 The Case with Nonnegative Equilibria
3.3.4 Stability via M-Matrix or Algebraic Inequality Methods
3.3.5 Stability via Matrix Inequalities or Mixed Methods
3.3.6 Topics on Robust Stability of RNNs
3.3.7 Other Topics on Stability Results of RNNs
3.3.8 Qualitative Evaluation on the Stability Resultsof RNNs
3.4 Necessary and Sufficient Conditions for RNNs
3.5 Summary
References

4 Delay-Partitioning-Method Based Stability Results for RNNs
4.1 Introduction
4.2 Problem Formulation
4.3 GAS Criteria with Single Weighting-Delay
4.3.1 Weighting-Delay-Independent Stability Criterion
4.3.2 Weighting-Delay-Dependent Stability Criterion
4.4 GAS Criteria with Multiple Weighting-Delays
4.5 Implementation of Optimal Weighting-Delay Parameters
4.5.1 The Single Weighting-Delay Case
4.5.2 The Multiple Weighting-Delays Case
4.6 Illustrative Examples
4.7 Summary
References

5 Stability Criteria for RNNs Based on Secondary Delay Partitioning
6 LMI-Based Stability Criteria for Static Neural Networks
7 Multiple Stability for Discontinuous RNNs
8 LMI-based Passivity Criteria for RNNs with Delays
9 Dissipativity and Invariant Sets for Neural Networks with Delay
10 Synchronization Stability in Complex Neural Networks
11 Stabilization of Stochastic RNNs with Stochastic Delays
12 Adaptive Synchroruzation of Complex Neural Networks
Index