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Qualitative Analysis and Control of Complex Neural Networks with Delays

Part of the Studies in Systems, Decision and Control Book Series (volume 34)

DOI: 10.1007/978-3-662-47484-6

ISBN: 978-3-662-47483-9

Publisher: Springer Berlin Heidelberg - Springer Journals

Jul 19, 2015

1 - 10 of 12 Chapters

LitStream

Chapter 1Introduction to Neural Networks

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 1 –36

[Analog circuits have played a very important role in the development of modern electronic technology. Even in our digital computer era, analog circuits still dominate such fields as communications, power, automatic control, audio, and video electronics because of their real-time signal...
LitStream

Chapter 2Preliminaries on Dynamical Systems and Stability Theory

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 37 –90

[In this chapter, we will review some fundamental concepts on dynamical systems and stability theory, and give some evaluations and opinions on some problems, which will be helpful for understanding the main contents of this book.]
LitStream

Chapter 3Survey of Dynamics of Cohen–Grossberg-Type RNNs

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 91 –172

[In Chaps. 1 and 2, we have introduced the history of artificial neural networks and the concepts of dynamical systems and stability, respectively, which are related to the research background of complex neural networks and the basis of qualitative stability analysis in the mathematical meaning.]
LitStream

Chapter 4Delay-Partitioning-Method Based Stability Results for RNNs

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 173 –204

[Chapter 3 has presented many ways on how to use the time delay to establish the effective stability criteria for RNNs with delays. In this chapter, inspired by the discussion in Chap. 3, a new delay splitting method is proposed. By nonuniformly splitting the interval of time delay through...
LitStream

Chapter 5Stability Criteria for RNNs Based on Secondary Delay Partitioning

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 205 –224

[Chapter 4 has presented a new way to establish the delay-dependent stability results for RNNs with delay. The main feature of the method in Chap. 4 is to split the time delay with fixed intervals by inserting some virtual sampling points or weighting coefficients, which leads to the nonuniformly...
LitStream

Chapter 6LMI-Based Stability Criteria for Static Neural Networks

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 225 –237

[In Chaps. 1 and 5, stability problems based on LMI have been investigated for a kind of local field RNNs with delay.]
LitStream

Chapter 7Multiple Stability for Discontinuous RNNs

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 239 –257

[In those network models, the considered activation functions in RNNs are continuous.]
LitStream

Chapter 8LMI-based Passivity Criteria for RNNs with Delays

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 259 –276

[As one of most widely used qualitative characteristics, stability property are studied for the equilibrium point of some kinds of RNNs with delays in Chaps. 4–7. For a dynamical system, there are many qualitative characteristics to be studied. In this chapter, we will study the passivity problem...
LitStream

Chapter 9Dissipativity and Invariant Sets for Neural Networks with Delay

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 277 –309

[Energy dissipation is a fundamental concept in dynamical systems. Passivity and dissipativity characterize the “energy” consumption of a dynamical system and form a powerful tool in many real applications. Passivity is closely related to stability and exhibits a compositional property for...
LitStream

Chapter 10Synchronization Stability in Complex Neural Networks

Wang, Zhanshan; Liu, Zhenwei; Zheng, Chengde

Pages: 311 –331

[In Chaps. 4–9, all the considered RNN models can be described as some state-vector differential equations, which can also be regarded as isolated systems or node systems. With the information communications and region interconnections being quickly developed, some isolated systems are coupled...

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