Finite/Fixed/Prescribed-time Stabilization And Synchronization Of Memristor Neural Networks By Interval Matrix Method

With the development of systems science,the structure,dynamics,regulation,and interconnection of neural networks have become one of the current hot topics of research,among which how to improve the computational and storage capacity of neural networks has become an urgent problem.As a new type of computational component,memristors are non-volatility,low power consumption,and highly integrated,which can better simulate human brain synapses.Therefore,the analysis and control of the dynamics of memristor neural networks have great importance and practical application,especially the finite/fixed/prescribed-time stabilization and synchronization control,which coincides with the research on the structure-function relationship,evolution,and regulation of systems in systems science.Nowadays,there are still a lot of challenging and explorable issues regarding the finite/fixed/prescribed-time stabilization and synchronization of the memristor neural network.For example,memristor neural networks are a class of state-dependent switching systems,how to solve the mismatch problem of memristor parameter switching? How to save the economic cost of control and make the memristor neural network achieve finite/fixed/prescribed-time stability and synchronization? How to overcome the instability and oscillation of the memristor neural network due to time delay? With these questions in mind,this paper investigates the dynamical behavior of finite/fixed/prescribed-time stabilization and synchronization of memristor neural networks by interval matrix method and applies the resulting theory to secure communication.The main contents and innovations of this paper are as follows.(1)For a class of stochastic interval time-delay systems,the interval parameters are represented by endpoint information based on the convex analysis principle,and the interval matrix method is proposed.By using It(?) differential formula and inequality analysis method,several Lyapunov-Krasovskii functions are constructed,and a nonlinear state delay feedback controller is designed.A sufficient condition for the stochastic finite time stability of the closed-loop stochastic delay interval system is obtained.The conclusion is applied to an energy storage circuit for numerical simulation to demonstrate the validity of the theoretical results obtained.(2)Finite-time synchronization of drive-response memristor neural networks without and with time-varying delays is investigated by the interval matrix method.By using the interval matrix method,the memristor neural network is transformed into a class of systems with interval parameters.By designing two kinds of nonlinear feedback controllers and combining them with the linear matrix inequality technique,sufficient conditions for the finite time synchronization of the drive-response memristor neural networks are obtained,and the upper bound of the settling time function is estimated.Two examples of numerical simulation demonstrate the correctness of the theory and the effectiveness of the controller.(3)For a class of inertial memristor neural networks with time-varying delay,we transform the inertial memristor neural networks into a class of systems with uncertain terms by the convex combinatorial transformation of matrices to handle the parameter switching of the memristors,and then reduce the second-order differential system to the first-order differential system by using the reduced-order method to obtain some sufficient conditions for finite-time stability of delayed inertial memristor neural networks and give the upper bound of the settling time functions.The two types of feedback controllers with different ways of handling time-varying delay terms are designed to ensure the finite-time stability of the inertial memristor neural network.Finally,two examples of numerical simulations are given to verify the accuracy of the theoretical results.(4)In this paper,the finite/fixed-time synchronization of time-varying delayed inertial memristive neural networks based on the interval matrix method is investigated in a unified framework.Different mathematical techniques are used in this paper to solve the mismatch problem of the memristor parameter switching,one is the maximum absolute value method and the other is the interval matrix method,while two different control strategies are designed to obtain different sufficient conditions in a unified framework,one in algebraic form and the other in linear matrix inequality form,to estimate the upper bound of the settling time.Finally,two numerical simulation examples illustrate that the interval matrix method has a faster convergence rate than the maximum absolute value method,and the theoretical results are applied to secure communications.(5)In this paper,the stochastic finite/fixed/prescribed-time stability of stochastic memristor neural networks with time-varying delays is studied under the unified framework.By properly adjusting the parameters of the controller,the system achieves stochastic finite-time stability,stochastic fixed-time stability,and stochastic prescribed-time stability without designing other controllers.Subsequently,the PI controller is improved to a suitable adaptive PI controller,sufficient criteria for stochastic finite/fixed/prescribed-time stability are obtained,and the upper bound of settling time is estimated.Finally,two examples are given to verify the feasibility of the theoretical results.