This article is concerned with the quantized fault-tolerant control (FTC) for consensus of multiple Lagrangian systems subject to stochastically switching networks, actuator and sensor faults. First of all, a reliable quantized FTC algorithm is developed under Markov jump networks (MJNs), where the communication signal is first quantized before transmitted to develop controllers, and the communication networks are stochastically switching with the sojourn time belonging to an exponential distribution. Then, to handle the FTC problem in the presence of unknown control directions, the Nussbaum function is introduced to further improve the control reliability. Furthermore, the FTC case involving semi-Markov jump networks (S-MJNs) and time-varying communication delays is considered, where the negative constraints of time delays can be effectively attenuated with the sojourn time following a Weibull distribution. Meanwhile, several sufficient criteria on the consensus analysis and algorithms synthesis are established by means of the Lyapunov–Krasovskii stability method. Finally, numerous illustrative examples are elaborated on for demonstrating the feasibility of the derived results.

中文翻译：

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受交换网络影响的多个拉格朗日系统的量化容错共识

本文关注的是量化容错控制 (FTC)，用于在随机切换网络、执行器和传感器故障的情况下使多个拉格朗日系统达成共识。首先，在马尔可夫跳跃网络（MJNs）下开发了一种可靠的量化 FTC 算法，其中通信信号在传输到开发控制器之前首先被量化，并且通信网络随着停留时间随机切换属于指数分布。然后，为了处理未知控制方向下的FTC问题，引入Nussbaum函数进一步提高控制可靠性。此外，还考虑了涉及半马尔可夫跳跃网络 (S-MJN) 和时变通信延迟的 FTC 情况，其中时间延迟的负面约束可以通过遵循威布尔分布的逗留时间有效地减弱。同时，通过Lyapunov-Krasovskii稳定性方法建立了关于一致性分析和算法综合的几个充分标准。最后，详细说明了许多说明性示例，以证明导出结果的可行性。