An extended generalized integral inequality based on free matrices and its application to stability analysis of neural networks with time-varying delays |
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| Institution: | 1. College of Science, Guilin University of Technology, Guilin, Guangxi 541004, PR China;2. School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541006, PR China;3. College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China;4. School of Information Science and Engineering, Chengdu University, Chengdu, Sichuan 610106, PR China;1. School of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China;2. Anhui Provincial Engineering Laboratory on Information Fusion and Control of Intelligent Robot, Wuhu 241000, China;3. School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China;4. Faculty of Automation, Huaiyin Institute of Technology, Huaian 223001, China;5. School of Engineering, Huzhou University, Huzhou 313000, China;1. School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea;2. Center for Global Converging Humanities, Kyung Hee University, Yongin 17104, Republic of Korea;3. School of the Information and Communication Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea |
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| Abstract: | This paper proposes an extended generalized integral inequality based on free matrices (EGIIFM) and applies it to the stability analysis of neural networks with time-varying delays. The EGIIFM estimates an upper bound for a quadratic form of a positive definite matrix with an augmented vector staked not only with the state and its derivative but also with the nonlinear activation function. By reflecting the correlated cross-information among the terms in the augmented vector as free matrices, the EGIIFM provides a tighter upper bound and encompasses various existing single integral inequalities as special cases. In addition, by establishing a new double integral Lyapunov–Krasovskii functional including the correlated cross-information, a less conservative stability criterion is obtained. Through three well-known numerical examples, the effectiveness of the EGIIFM is evaluated. |
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