School of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China.
School of Science, Yanshan University, Qinhuangdao 066004, China.
Neural Netw. 2021 Jul;139:335-347. doi: 10.1016/j.neunet.2021.03.033. Epub 2021 Apr 1.
This paper is concerned with the global synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights, where the dynamic nodes are modeled to be discontinuous, and subject to the local Hölder nonlinear growth in a neighborhood of continuous points. Firstly, an inequality with respect to variable-order fractional derivative for convex functions is proposed. On the basis of the proposed inequality, a global convergence principle in finite time for absolutely continuous functions is developed. Secondly, based on proposed convergence principle in finite time, a new sliding mode surface is presented, and an appropriate sliding mode control law is designed to drive the trajectory of the error system to the prescribed sliding mode surface in finite time and remain on it forever. In addition, on the basis of differential inclusions theory and Lur'e Postnikov-type convex Lyapunov function approach, the sufficient conditions with respect to the global stability in finite time are established in terms of linear matrix inequalities for the error system on designed sliding mode surface. Moreover, the upper bound of the settling time is explicitly evaluated. Finally, the effectiveness and correction of synchronization strategies are illustrated through two simulation experiments.
本文研究了具有多权重的变阶分数阶复动态网络的有限时间全局同步问题，其中动态节点被建模为不连续的，并在连续点的邻域内受到局部 Hölder 非线性增长的影响。首先，提出了一个关于凸函数的变阶分数阶导数的不等式。在此基础上，发展了绝对连续函数的有限时间全局收敛原理。其次，基于提出的有限时间收敛原理，提出了一个新的滑模面，并设计了一个合适的滑模控制律，以使误差系统的轨迹在有限时间内驱动到预定的滑模面，并永远保持在其上。此外，基于微分包含理论和 Lur'e Postnikov 型凸 Lyapunov 函数方法，以线性矩阵不等式的形式给出了误差系统在设计的滑模面上的有限时间全局稳定性的充分条件。此外，还明确评估了 Settling 时间的上界。最后，通过两个仿真实验验证了同步策略的有效性和正确性。
