时滞扩散性复杂网络同步保性能控制

摘要

The problem of guaranteed cost synchronization control is investigated, mainly aiming at nodes expanding in complex dynamical networks with time delay. Firstly, with the method of the adaptive dynamic feedback controller, the sufficient conditions for the existence of the guaranteed cost controller with time delay in complex network are obtained based on the Lyapunov0s stability theory and the method of matrix inequality. Then, an impulse controller is designed to achieve synchronization with the principle of pinning control when the system nodes are expanding under the condition that the original adaptive controller cannot make the synchronization of the system. The designed adaptive dynamic feedback controller makes the performance index of the system meet certain requirements under the condition of ensuring the asymptotic stability of the system. Finally, a numerical example is given to demonstrate the feasibility of proposed method.%针对节点扩张的时滞复杂网络系统，在节点扩张的条件下，讨论此类系统的同步保性能控制问题。首先采用自适应控制方法，利用Lyapunov-Krasovskii 稳定性理论，结合矩阵不等式的凸优化问题处理方法，得出了时滞复杂网络系统保性能控制器存在的充分条件；当系统节点的扩张后，在原有自适应控制器不能使系统同步稳定的条件下，设计脉冲控制器，利用牵制控制原理使系统达到稳定同步。所设计的自适应动态反馈控制器在保证系统的渐近稳定条件下使系统性能指标满足一定的要求。最后给出一个数值仿真说明其有效性。