具有随机马尔可夫时延的网络控制系统H∞故障检测

针对存在随机时延的网络环境，研究了一类网络控制系统的H∞故障检测滤波器设计问题．考虑了可 由马尔可夫过程描述的随机时延，网络控制系统被建模成离散时间有限状态的马尔可夫跳变线性系统．基于此类模 型，构造了系统的残差发生器，相应的故障检测问题转化为H∞滤波问题．通过选择合适的滤波器增益，使得残差和 故障之间的误差尽可能地小，保证了残差对于未知输入的鲁棒性．以线性矩阵不等式的形式给出了故障检测滤波器 存在的充分条件，并运用锥补线性化方法完成了滤波器设计过程．数值算例表明，上述网络控制系统故障检测滤波 器不仅对故障敏感，同时对外界扰动具有鲁棒性．

H_∞ Fault Detection for Networked Control System with Random Markov Delays

With the presence of random time-delay introduced by the network, the problem of H_∞ fault detection filter design for a class of networked control systems is investigated. By considering random time-delay that could be described as a Markov process, the networked control system is modeled as discrete-time, finite-dimensional Markov jump linear system.The residual generator is constructed based on this model. The corresponding fault detection problem is formulated as an H_∞ filtering problem. Through appropriate choice of the filter gain, the error between residual and fault is made as small as possible which ensure robustness of the residual against unknown inputs. A sufficient condition to solve this problem is given in terms of the linear matrix inequalities, and the filter design procedure is proposed via the cone complementarity linearization method. The numerical example shows that the proposed fault detection filter is sensitive to the fault but robust to exogenous disturbance.