Abstract: Considering the random phenomenon of sensor failure, actuator failure and networked time-delay, the independent Bernoulli random sequences as switching matrices of sensor failure, actuator failure are introduced. The time-delay’s variation interval is divided into two subintervals, introducing the Bernoulli random variation and transforming the probability distribution into parameter matrices. The random networked control system modeled is constructed. The problem of random fault-tolerant control with the existence of sensor failure and actuator failure for the system is investigated. Based on Lyapunov stability theory, combined with linear matrix inequality technology, the conditions for this system to be exponential stable in mean square sense are derived. These conditions depend on time delays probability distribution as well, not just depend on time-delay’s maximum and minimum bounds. At the end, a numerical example is given to illustrate the validity of the main results.

Key words: depend on probability distribution, time-delay dividing, networked systems, random fault-tolerant design

摘要： 针对网络控制系统的传感器、执行器和网络时延具有随机性这一现象，引入相互独立的Bernoulli随机变量序列作为传感器失效故障、执行器失效故障的开关矩阵，将时延的变化区间任意分成两个小区间，引进Bernoulli随机变量并将其概率分布引入到系统矩阵中，建立随机的网络化控制系统模型，研究了该系统存在传感器失效故障、执行器失效故障及二者同时失效故障情况下的随机容错控制问题。基于Lyapunov稳定性理论，结合线性矩阵不等式技术，给出了确保系统均方指数稳定的条件，该条件不仅依赖于时延的上下界，还依赖于时延的概率分布。数值实例说明结论是有效的。

关键词: 概率分布依赖, 时滞拆分, 网络化系统, 随机容错设计