Research On The Dissipativity Of Memristive Neural Networks With Time Delays

As the memristor was found,the research on the dynamics of memristive neural networks has attracted wide attention in academic circles.Memristive neural networks are state-dependent differential dynamical systems which are switching and influenced by some factors such as the nonlinear characteristics of the systems themselves and dif-ferent levels of combination and so on.Therefore,their dynamic behaviors are complex and difficult to deal with.However,owe to the trend of application of memristor in industrial engineering,it is urgently necessary to complete memristive neural networks'dynamic theory which provides important theoretical basis and technical paths for various applications of memristive neural networks.Besides,because time delay is an important factor affecting systems'instability and dissipative properties are widely used in dynamic systems such as stability analysis,chaos control,synchronization,signal processing and fuzzy control and so on,the research on the dissipativity of memristive neural networks with time delays has become an important topic.In recent years,many scholars in the world have given many good methods and obtained the related conditions of dissipativity for neural networks with time delays.Based on both nonsmooth analysis and Lyapunov method,we construct the appropri-ate Lyapunov-Krasovskii functional and derive the less conservative criteria by applying the theoretical analysis of the linear matrix inequality and numerical examples in this paper.The contents of this research and main results are as follows:1.The problem of passivity analysis is studied for memristive neural networks with leakage and time-varying delays.By combining differential inclusions with set-valued maps,the system of memristive neural networks is converted into the conventional one.By adding a triple quadratic integral and relaxing the requirement for the positive definite-ness of some matrices,a proper Lyapunov-Krasovskii functional is constructed.Based on the establishment of the novel Lyapunov-Krasovskii functional,the new passivity criteria are acquired by mainly applying Wirtinger-based double integral inequality,S-procedure and so on.Moreover,the conservatism of passivity conditions can be reduced.Final-ly,four numerical examples are given to show the effectiveness and rationality of the proposed criteria.Further,it is not difficult to find that this result greatly reduces the conservatism by comparison with the ones of the existing literature.2.The problem of passivity analysis is investigated for memristive neural network-s with interval multiple time-varying delays.By combining differential inclusions with set-valued maps,the system of memristive neural networks is changed into the conven-tional one.By adding several triple quadratic integrals,a proper Lyapunov-Krasovskii functional is constructed.Based on the establishment of the novel Lyapunov-Krasovskii functional,the new passivity criteria are gained by mainly applying first-order recipro-cally convex method,second-order reciprocally convex method,free-weighting matrices technique and zero equalities.Finally,two numerical examples are given to show the effectiveness and less conservatism of the proposed criteria.Further,it is not difficult to find that this result greatly reduces the conservatism by comparison with the ones of the existing literature.3.The problem of strict?Q,S,R?-?-dissipativity analysis is discussed for memris-tive neural networks with leakage and time-varying delays.The performance of?Q,S,R?-?-dissipativity is more general than the passivity.By combining differential inclusions with set-valued maps,memristive neural networks are converted into the conventional neural networks.Based on the construction of a novel Lyapunov-Krasovskii functional,the relaxed dissipativity criteria are obtained by combing Wirtinger-based integral in-equality with free-weighting matrices technique.Specially,this proposed criteria do not really require all the symmetric matrices involved in the employed quadratic to be posi-tive definite.Moreover,the obtained criteria are less conservative.Finally,two numerical examples are given to show the effectiveness and less conservatism of the proposed cri-teria.Further,it is not difficult to find that this result greatly reduces the conservatism by comparison with the ones of the existing literature.4.The problem of extended dissipative conditions is researched for memristive neural networks with multiple time delays.The multiple time delays contain discrete,distributed and leakage time-varying delays.Based on both nonsmooth analysis and Lya-punov method,the extended dissipative conditions are gotten by mainly applying dif-ferential inclusions,set-valued maps and some new integral inequalities.The extended dissipative conditions can be applied in judging l₂-l_?performance,H_?action,passive behavior and dissipative dynamics in a unified framework.Finally,two numerical exam-ples are provided to demonstrate the effectiveness and rationality of the derived results.