Research On Guaranteed Cost Control Of Uncertain Complex Dynamical Network With Delay

Complex network is a new discipline to study the complex systems，it combinesmathematics, statistical physics and nonlinear system theory and other disciplines. Theresearch on complex network has attracted experts and scholars in differentfields.Many systems in the real world can be seen as a network, such as electricitynetworks, Internet，transport networks, personal networks,etc., so the study of thetopology structure and dynamical behavior of complex networks has greatsignificance.A review of the development process,research status and related control methodof complex network are briefly introduced. This paper gives the description of thegeneral dynamics of complex network, and studies the dynamic behavior and controlmethods.Firstly, the synchronization dynamical behaviors of uncertain complex networkare discussed.Using Lyapunov stability theory, local and global networksynchronization algorithm are proposed separately.An adaptive feedback controlleris designed to make the network achieve local and global synchronization status.Toconfirm the result,the famous Lorenz system is stimulated as the nodes of thecomplex networks.Secondly, based on the existing research results, we combine algebraic graph,control theory, the nonlinear system theory and matrix analysis with guaranteedcontrol of complex dynamic networks,it provids a theoretical basis for the followingresearch about guaranteed cost control of linear coupled complex networks andcomplex networks with coupling delay.Additionally,guaranteed cost control of linear coupled complex networks isstudied. For linear coupled complex network, using Kronecker product form canavoid the limitation caused by externalization method,because it does not need tolinearize the nonlinear function near the synchronization state of network. Thesuperiority and conservative of the results is increased.Finally,considering the delay factor in coupled complex networks, guaranteedcost control for complex networks with coupling delays is studied.The stabilitycondition and the guaranteed cost controller design method is derived in terms ofLyapunov stability theory.The state feedback controller with gain perturbations isdesigned to achieve the asymptotic stability of the system,and guarantee the performance index of closed-loop system satisfying certain bounds.