This paper is concerned with an observer-based robust $H_{\infty }$ synchronization problem for a class of fractional-order multi-weighted complex dynamical networks subject to Markovian jump parameters, actuator faults and time-varying coupling delay by using fault-tolerant control scheme. The considered actuator fault model is a general one, which consisting of both linear and nonlinear fault terms. Further, by employing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, a new set of sufficient conditions is derived to ensure the asymptotic synchronization of the addressed system in the mean square sense with a prescribed $H_{\infty }$ performance index. In particular, by constructing monochromatic Lyapunov functional and utilizing extended Wirtinger-based integral inequality the required sufficient conditions are developed in terms of linear matrix inequalities. Finally, two numerical examples including financial model are provided to illustrate the effectiveness of the obtained results.

本文关注的是基于观察者的鲁棒性 $H_{\infty }$利用容错控制方案解决了一类受马尔可夫跳跃参数、执行器故障和时变耦合延迟影响的分数阶多加权复杂动态网络的同步问题。所考虑的执行器故障模型是一种通用的模型，它包括线性和非线性故障项。此外，通过采用连续频率分布等效模型并使用间接李雅普诺夫方法，推导出一组新的充分条件，以确保所寻址系统在均方意义上具有指定的渐近同步$H_{\infty }$性能指标。特别是，通过构造单色李雅普诺夫函数并利用扩展的基于 Wirtinger 的积分不等式，根据线性矩阵不等式开发了所需的充分条件。最后，提供了包括财务模型在内的两个数值例子来说明所得结果的有效性。