Multi-performance Analysis And Synthesis Of Markov Jump Memristive Neural Networks

In this paper,the powerful high-speed parallel processing capability of the neural network and the memorizer's natural information processing and storage functions are combined to build and expand the existing memristor-based neural network model.By introducing the idea of“Markov switching”,considering the unavoidable time-varying delays in the actual systems,the global dissipative exponential stabilization analysis,mixedH_?/l₂-l_?state estimation,and non-fragile synchronous dissipative control for the model under consideration are addressed.The main conclusions are as follows:1.Global exponential stabilization analysis for a class of Markovian jump memris-tive neural networks with time-varying delays is investigated.In order to obtain a more realistic model of the system,this paper will introduce the random variables conforming to the Bernoulli distribution type into the construction of system,so that some actual sit-uation of the system can occur at a certain probability.Under the framework of Filippov's solution,a memristor-based neural network is transformed into interval parameter system.Based on Lyapunov stability principle,combining free-weight matrix and improved Jen-sen inequality techniques,the delay-dependent criterion of the global exponential stabili-zation of the memristive neural networks is analyzed and derived.At the same time,the relevant criterion is transformed into the form of linear matrix inequality.In this paper,a full simulation is performed to verify the correctness of the conclusions,where the com-parison with the existing literatures shows the superiority of the proposed method.In brief,the analysis method of this paper reduces the limitation of the upper bound of the deriva-tive of time-varying delay in continuous time-delay systems to some extent,which com-plements and extends the existing theory of time-delay systems.2.For a class of Markovian jump memristive neural networks with time-varying delays,the mixedH_?/l₂-l_?state estimation is performed.Under the framework of Filippov's solution,a memristor-based neural network is transformed into a range param-eter system.Then,based on Lyapunov functional method,the integrals of functional de-rivatives are dealt with by the technique of the reciprocally convex combination and free weight matrix,and a new criterion for ensuring the global asymptotic stability of the error system with a specified performance index is obtained.Further,a novel decoupling method is used to give an explicit expression of the state estimator gain.Compared with the existing results,this method can effectively improve the control income and reduce the cost of control.Finally,an numerical simulation is provided to demonstrate the valid-ity of the theoretical results.3.A non-fragile dissipative synchronous gain-scheduled control for a class of Markovian jump memristive neural networks with time-varying delays is concerned.By introducing an appropriate Lyapunov function with improved integral inequalities and combining with the reciprocally convex combination technique,the low-conservation time-dependent synchronization conditions of the system are deduced by using the information of the upper and lower bounds of the time-varying delays of the system.Based on these criteria,an effective synchronous control strategy is proposed to obtain the desired non-fragile gain-gain controller and achieve asymptotical synchronization between the master and slave systems.Finally,simulation results,tables,and dendrograms are used to verify the advantages of the obtained results and the feasibility of theoretical research.