This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results.

本文研究了一类具有多权重、时变耦合延迟和外部干扰的复杂动态网络的鲁棒同步问题。具体来说，增益波动出现在所提出的控制器中，并以服从伯努利分布的随机变量表示。本文的主要目的是设计一个非脆弱记忆状态反馈控制器，使得产生的误差系统在规定的条件下随机同步 表现水平 . 首先，构造 Luenberger 型状态观测器来估计寻址系统的状态变量。其次，通过构建适当的 Lyapunov-Krasovskii 泛函并使用基于 Wirtinger 的积分不等式技术，以线性矩阵不等式的形式建立所提出系统同步所需的一组充分条件。最后，提供了两个数值例子来证明所开发的理论结果的有效性和可行性。