Research On The Stabilization And Synchronization Of Time-Delay Systems With Sampled-Data Control

With the rapid growth of communication technology,digital technology and highspeed computers,sampled-data control has garnered wide-scale attention.In the implementation of sampled-data control,only the sampled information of a system at its sampling instants is transmitted to the controller.Thus,sampled-data control can effectively save the limited network communication resource by reducing the transmission information.Meanwhile,due to the finite speed of execution of system component and congestion during signal acquisition and transmission,time delay is inescapable encountered in many dynamical systems.However,time delay may cause oscillation,instability and divergence to seriously deteriorate system performance.Hence,it is profound to investigate the dynamical behaviors and controller design of time-delay systems.We focus on,in this thesis,the stabilization and synchronization problems of four typical timedelay systems: time-delay memristive neural networks,inertial neural networks,chaotic Lur’e systems,and complex networks.The main works are given as:1.By sampled-data control,the stabilization problem has been investigated for timedelay memristive neural networks.First,by a new technique,the concerned time-delay memristive neural networks are converted into traditional neural networks with uncertain parameters.Next,the sampled-data controller is designed via the event-triggered mechanism,which effectively saves the limited network communication resource.Then,by constructing a augmented Lyapunov-Krasovskii functional,sufficient conditions are derived to ensure the stability and stabilization of the time-delay memristive neural networks.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed theory results.2.By sampled-data control,the synchronization problem has been investigated for time-delay inertial neural networks.First,by introducing a variable transformation,the second derivative time-delay inertial neural networks are converted to two first derivative systems.Next,the sampled-data controller is designed via the quantizer,which effectively reduces the utilization of bandwidth.Then,by proposing an inequality to deal with the heterogeneous time delays and constructing an appropriate Lyapunov-Krasovskii functional,new synchronization criteria are established for time-delay inertial neural networks.Finally,a numerical example is given to verify the effectiveness and less conservativeness of the obtained theory results.3.By sampled-data control,the synchronization problem has been investigated for time-delay chaotic Lur’e systems.Firstly,the extended Wirtinger-inequality-based Lyapunov-Krasovskii functional approach is proposed.This approach grasps more sampling information by introducing more free matrices.Secondly,a zero equality is introduced,which can make full use of the information of system at the dynamic partitioning point.Thirdly,based on the zero equality and the proposed functional approach,new synchronization criteria are derived for time-delay chaotic Lur’e systems.Finally,the superiorities and effectiveness of the theory results are verified by Chua’s circuit and fourth-order Matsumoto-Chua-Kobayashi(MCK)circuit.4.By sampled-data control,the synchronization problem has been investigated for time-delay complex networks.Firstly,with the influence of random and parameter disturbance phenomena,the sampled-data controller is designed.Secondly,a LyapunovKrasovskii functional with cubic sawtooth structure term is constructed,which can fully capture the sampling information.Thirdly,based on the Lyapunov-Krasovskii functional,new synchronization criteria are established for time-delay complex networks.Finally,two numerical examples are given to illustrate the effectiveness of the obtained theory results.It is worth mentioning that:(1)the sampled-data controller with randomly occurring controller gain fluctuations is more applicable than some existing ones;(2)the constructed Lyapunov-Krasovskii functional only needs to be positive definite at sampling instants.5.By sampled-data control,the synchronization problem has been investigated for complex networks with partial couplings.Firstly,by the regrouping approach,the concerned complex networks with partial couplings are deformed according to the channels.Secondly,under nonuniform sampling,a new event-triggered event-triggered mechanism is newly proposed.Based on this mechanism,the sampled-data controller is designed.Thirdly,by a Lyapunov-Krasovskii functional with input-delay-product-type term,new criteria are derived to synchronize the complex networks with partial couplings.Finally,two simulation examples are provided to illustrate the merits and effectiveness of the theory results.