The guaranteed cost synchronization control problem of some general complex dynamical networks with time delay is investigated. A dynamic feedback controller is designed for the system guaranteed cost synchronization. Meanwhile, due to many nodes in the complex networks and the complex of the direct control, use of the the pinning control to make the system achieve guaranteed cost synchronization is also investigated. Based on the Lyapunov stability theory and the matrix inequality, the sufficient conditions are obtained for the existence of the guaranteed cost controller with time delay in complex network. The dynamic feedback controller is designed to ensure the asymptotic stability conditions of the system and make the performance index of the system meet certain requirements. Finally, the feasibility of the proposed method is demonstrated by numerical examples.
In this study, we elucidated the exponential synchronization of a complex network system with time-varying delay. Then the exponential synchronization control of several types of complex network systems with time-varying delay under no requirements of delay derivable were explored. The dynamic behavior of a system node shows time-varying delays. Thus, to derive suitable conditions for the exponential synchronization of different complex network systems, we designed a linear feedback controller for linear coupling functions, using the Lyapunov stability theory, Razumikhin theorem, and Newton-Leibniz formula. The exponential damping rates for the exponential synchronization of different complex network systems were then estimated. Finally, we validated our conclusions through a numerical simulation.
This paper focuses on the global exponential synchronization problem of nonlinearly coupled complex dynamical networks with time-varying coupling delays. Several simple and generic global exponential synchronization criteria are derived based on the Lyapunov stability theory and the Dini derivatives using the Halanay and generalized Halanay inequalities. These criteria rely on system parameters alone and can be used conveniently in practical applications. In addition, the system parameters do not satisfy the conditions of the proposed criteria. That is, the system itself cannot synchronize. However, system synchronization can be achieved by adding the appropriate feedback controllers, thereby providing a practical and effective control method for complex dynamical networks. An estimation method of exponential convergence rate is also presented. Finally, the effectiveness of the proposed criteria is verified through numerical simulations.
This study examines finite-time synchronization for a class of N-coupled complex partial differential systems (PDSs) with time-varying delay. The problem of finite-time synchronization for coupled drive-response PDSs with timevarying delay is similarly considered. The synchronization error dynamic of the PDSs is defined in the q-dimensional spatial domain. We construct a feedback controller to achieve finite-time synchronization. Sufficient conditions are derived by using the Lyapunov-Krasoviskii stability approach and inequalities technology to ensure that the proposed networks achieve synchronization in finite time. The proposed systems demonstrate extensive application. Finally, an example is used to verify the theoretical results.
A kind of H ∞ non-fragile synchronization guaranteed control method is put forward for a class of uncertain time-varying delay complex network systems with disturbance input. The network under consideration includes unknown but bounded nonlinear coupling functions f (x) and the coupling term and node system with time-varying delays. The nonlinear vector function f (x) need not be differentiable but should satisfy the norm bound. A non-fragile state feedback controller of the gain with sufficiently large regulation margin is designed. It is ensured that the parameters of the controller could still be effective under small perturbation. The sufficient conditions for the existence of H ∞ synchronous non-fragile guaranteed control of this system have been obtained by constructing a suitable Lyapunov-Krasovskii functional, adopting matrix analysis, using the theorem of Schur complement and linear matrix inequalities (LMI). These conditions can guarantee robust asymptotic stability for each node of network with disturbance as well as achieve a prescribed robust H ∞ performance level. Finally, the feasibility of the designed method is verified by a numerical example.
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