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Basic theorem and global exponential stability of differential-algebraic neural networks with delay
Jiejie Chen1, Boshan Chen2, Zhigang Zeng3
1The College of Computer Science and Information Engineering, Hubei Normal University, Huangshi 435002, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
Abstract:
A differential-algebraic neural network (DANN) with delay (DDANN) is proposed. Firstly, the global existence and uniqueness theorems are established for a DDANN, respectively. Next, a new differential-algebraic inequality is established. Then, a theorem on global exponential stability of DDANN is shown by using this inequality. As an application of DDANN, a very concise criterion on global exponential stability for a neutral-type neural network is given by using DDANNs. Finally, two examples are given to illustrate the theoretical results.
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