Global polynomial stabilization of proportional delayed inertial memristive neural networks.

• The paper is the first batch that tries to inquiry the GPS of the PDIMNNs. Furthermore, unlike the previous literature [11,21,35] , the nonlinear substitution that converts the PDs system to a constant delays system is not used. Because the subsequent pro-cessing of the converted system is complicated, this paper directly performs on the original PDs system. • The paper employs the non-reduced-order method, which r-efrains the double-dimensional problem after reduced-order [3–5,23,24]. In practical applications, the method is more ponderable and si-gnificative for second-order scheme under controller. • In the paper, devise both the feedback controller and the adaptive controller for the first time to achieve the GPS of the PD-IMNNs. The advantages of the two types of controllers are compar-ed through numerical examples and simulations. The mathematical model is closer to reality, and selecting the appropriate controller in application can further reduce control expenses. This article probes into the global polynomial stabilization (GPS) of proportional delayed inertial memristive neural networks (PDIMNNs). Here, ruling out the reduced-order way, discuss the GPS of PDIMNNs under the second-order scheme directly. Firstly, a feedback controller is designed to make the system self-stabilizing. By designing suitable Lyapunov functional with adjustable parameters and combining with inequality techniques, two algebraic criteria are obtained to realize the GPS of the PDIMNNs. Owing to the conservatism caused by the ineluctable inequality scaling, it is worth noting that the controller gains are greater than the actual requirements. To further save control expenses, employing an adaptive controller to make the system stabilized. Finally, three numerical examples which sustain the usability of the obtained theoretical conclusions are shown. [ABSTRACT FROM AUTHOR]