Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 33, Issue 10, Pages 5656-5665Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2021.3071183
Keywords
Neural networks; Delay effects; Stability criteria; Power capacitors; Memristors; Lyapunov methods; Algebra; Complex-valued (CV) neural networks; dissipativity; memristive neural networks; quaternion-valued (QV) neural networks; stability
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Funding
- National Natural Science Foundation of China [12001452]
- Program of Science and Technology of Sichuan Province of China [2022NSFSC0532]
- Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province of China [2021ZYD0012]
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In this article, unified criteria for the global dissipativity and stability of delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) are analyzed. By establishing a unified model, applying the Lyapunov method, and solving mathematical difficulties, the derived criteria are shown to have advantages in smaller calculation, lower conservatism, more diversity, and higher flexibility. Two numerical examples are provided to demonstrate the effectiveness and improvements of the theoretical results.
The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.
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