Adaptive H_∞Synchronization For General Complex Networks With External Disturbance

In recent years, there have been a lot of research results on complex dynamical networks.However, few have taken disturbance into account. In fact, the complex network does notexist isolated in real life. The internal and external disturbances are common phenomenon in thecomplex networks. So, it is very important and significant for us to take attention to thesynchronous research for the complex dynamical networks with disturbance both in theory andin applications.In this paper, we will investigate the synchronization and control of complex dynamicalnetworks with disturbance. This paper focuses on the research of the " Adaptive H_∞synchronization for general complex networks with external disturbance " problem. The maincontents and innovation points are listed as follows.(1) We investigate the synchronization of two different general chaotic systems withexternal disturbances via the adaptive H_∞control technique. Based on the Lyapunov stabilitytheory and linear matrix inequality (LMI), several adaptive H_∞synchronization schemes areestablished which guarantee robust asymptotically synchronization for the drive system and thenoise-perturbed response system as well as achieving a prescribed robust H_∞performance level.Finally, the Lorenz system and the noise-perturbed R ssler system are taken as an example toanalyze the adaptive H_∞synchronization process. The numerical simulations have shown thecorrectness and effectiveness of the proposed methods.(2) The global adaptive H_∞synchronization is intensively investigated for general delayedcomplex dynamical networks. The network under consideration contains unknown but boundednonlinear coupling functions, time-varying delay, external disturbance. Based on the Lyapunovstability theory, linear matrix inequality (LMI) optimization technique combing with adaptivecontrol, several global adaptive H_∞synchronization schemes are established which guaranteerobust asymptotically synchronization for each node of noise-perturbed network as well asachieving a prescribed robust H_∞performance level. Finally, detailed and satisfactory numericalsimulations have validated the feasibility and the correctness of the proposed techniques.