Abstract
This study proposes further results for the stability analysis issue of uncertain delayed neural networks (UDNNs) via the reliable memory feedback control scheme. First, an improved quadratic function method is introduced for constructing a novel term V 1 x t , which can fully excavate some intrinsic relationships between the delay derivative information and time-delay information. Based on the time-delay-product function (TDPF) and linear convex combination method (LCCM), the information storage is further improved for obtaining new theoretical results. Second, by using resultful integral inequalities and correlation analysis approaches, several relaxed criteria are established with respect to the asymptotical stability of the considered UDNNs. Third, the desired reliable memory feedback controller (RMFC) is achieved, which can ensure the system stability of UDNNs. Lastly, two numerical experiments are given to illustrate the significance of the theoretical results.
Highlights
Because the structure of the NN model is similar to the synapse structure of the human brain, it can be described by a variety of differential equations [1,2,3,4,5,6,7]. e wide application of NNs in various fields has received widespread attention, such as signal processing [8], fault diagnosis [9], optimization problem solving [10], pattern recognition [11], image processing [12], and other fields [13,14,15,16]
Many researchers have made a lot of contributions of how to establish a suitable Lyapunov–Krasovskii functional (LKF) in order to better study the delayed systems [13, 34,35,36,37]
There are many methods to construct a reasonable LKF, but only increasing the cross-sectional area will hardly improve, and it will cause a heavy calculation burden [23, 38, 39]. erefore, the method of constructing LKF from a new perspective has become a hot issue in current research [34, 40]. rough in-depth study of existing work, this paper proposes an improved DTPF strategy to construct a new LKF, which fully considers information concerning time delays and the derivative information of both states and time delays, and the conservativeness of the guidelines can be further reduced. e issues discussed above have inspired the purpose of this study
Summary
Because the structure of the NN model is similar to the synapse structure of the human brain, it can be described by a variety of differential equations [1,2,3,4,5,6,7]. e wide application of NNs in various fields has received widespread attention, such as signal processing [8], fault diagnosis [9], optimization problem solving [10], pattern recognition [11], image processing [12], and other fields [13,14,15,16]. Rough in-depth study of existing work, this paper proposes an improved DTPF strategy to construct a new LKF, which fully considers information concerning time delays and the derivative information of both states and time delays, and the conservativeness of the guidelines can be further reduced. (1) A novel quadratic function V1(x (t)) is constructed via developing an improved TDPF approach, which can fully excavate some intrinsic relationships between the delay derivative information and the time delay (2) Based on this construction method of LKF, the information storage performance of the function is strengthened, an appropriate integral inequality and linear convex combination method are adopted, and a more conservative stability criterion is obtained (3) Different from the earlier work, this paper designs a new RMFC, which fully considers the effective transmission of the three state signals of the controller while enhancing the performance of the controller
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