Study On The Stability Of Impulsive Complex-Valued Neural Networks With Time Delays

Since 1980 s the mathematical model of neural network has been established by Hopfield who is the biophysicist at California Institute of Technology,a variety of neural networks have been proposed,one of them is complex-valued neural networks(CVNNs).Because CVNNs with complex-valued state,output,connection weight can deal with complex data directly,which is both natural and convenient,CVNNs has attracted the attention of scholars at home and abroad and has become a hot research field.In the design of CVNNs to solve practical problems,it is often necessary to analyze and discuss its stability and choose appropriate network parameters and activation functions to ensure the normal operation of the network.Therefore,it is of great significance to study the stability of complex-valued neural networks.The main contributions and originalities contained in thesis are as follows:(1)Global ?-stability of impulsive complex-valued neural networks with mixed time-varying delaysThe global ?-stability of impulsive complex-valued neural networks with mixed time-varying delays is investigated.For the considered complex-valued neural networks,the activation functions only need to satisfy the Lipschitz conditions.Based on the homeomorphism mapping principle in the complex domain,a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks was proposed in terms of linear matrix inequalities(LMIs).Through the construction of appropriate Lyapunov-Krasovskii functionals,and with the free weighting matrix method and inequality technique,a delay-dependent criterion for checking the global ?-stability of the complex-valued neural networks was established in LMIs.Finally,a simulation example was given to show the effectiveness of the obtained result.(2)Global stability of impulsive complex-valued neural networks with time delay on time scalesThe global stability of impulsive complex-valued neural networks with time delay on time scales is investigated.Based on the time scale calculus theory,both the continuous-time and discrete-time neural networks were described under the same framework.For the considered complex-valued neural networks,the activation functions need not be bounded.According to the homeomorphism mapping principle in the complex domain,a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks was proposed in complex-valued linear matrix inequalities(LMIs).Through the construction of appropriate Lyapunov-Krasovskii functionals,and with the free weighting matrix method and matrix inequality technique,a delay-dependent criterion for checking the global stability of the complex-valued neural networks was established in the complex-valued LMIs.Finally,a simulation example was given to show the effectiveness of the obtained result.(3)Global synchronization of complex-valued neural networks with leakage time delaysThe synchronization of complex-valued neural networks with leakage time delays was investigated.For the considered complex-valued neural networks,the activation functions need not be separated into real parts and imaginary parts.Through the construction of appropriate Lyapunov-Krasovskii functionals,and with the drive--response synchronization method,the free weighting matrix method and the matrix inequality technique,a delay-dependent criterion for checking the synchronization of complex-valued neural networks was established in the form of complex-valued linear matrix inequalities(LMIs),meanwhile the design method for the synchronization controllers was given.Finally,a simulation example showed the effectiveness of the present work.(4)Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effectsIn this paper,the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects was discussed.By employing Lyapunov-Krasovskii functional method and using matrix inequality technique,several sufficient conditions in the form of complex-valued linear matrix inequalities(LMIs)were obtained to ensure the existence,uniqueness and global exponential stability of equilibrium point for the considered neural networks.Moreover,the exponential convergence rate index was estimated,which depended on the system parameters.The proposed stability results were less conservative than some recently known ones in the literatures,which was demonstrated via two examples with simulations.(5)Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delaysThis paper investigated the stability problem for a class of impulsive complex--valued neural networks with both asynchronous time-varying and continuously distributed delays.By employing the idea of vector Lyapunov function,M-matrix theory and inequality technique,several sufficient conditions were obtained to ensure the global exponential stability of equilibrium point.When the impulsive effects were not considered,several sufficient conditions were also given to guarantee the existence,uniqueness and global exponential stability of equilibrium point.Two examples were given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results.