一类具有未知干扰的Markov跳变系统故障检测

针对一类具有未知扰动的Markov跳变系统的故障检测问题，设计出了系统的优化故障检测观测器．通过对系统进行重构，获取了包括未知扰动、建模误差等未知输入信号和故障信号的残差动态特性，分别选取残差的扰动信号和故障信号的能量范数指标来体现其对扰动的抑制作用和对故障的灵敏性，并将故障检测观测器的设计描述为一个优化问题．利用构造的Lyapunov函数和线性矩阵不等式，证明并给出了故障检测观测器有解的充分条件，提出了优化设计方法．所设计的观测器使系统具有随机稳定性，抑制干扰能力强，满足所给的范数指标．仿真算例结果表明，在故障发生时，优化观测器可以很灵敏地检测出故障，并能将未知扰动对残差的影响有效地抑制在给定的范围内。

Fault Detection for a Class of Markov Jump Systems with Unknown Disturbances

An optimized fault detection observer is designed for a class of Markov jump systems with unknown disturbances. By re-constructing the system, the residual error dynamic characteristics of unknown input and fault signals including unknown disturbances and modelling error are obtained. The energy norm indexes of disturbance and fault signals of residual error are selected separately to reflect the restraint of disturbance and the sensitivity of faults, and the design of fault detection observer is described as an optimization problem. By using the constructed Lyapunov function and linear matrix inequalities, a sufficient condition that the solution of the fault detection observer exists is given and proved, and an optimized design approach is presented. The designed observer makes the systems have random stability and better cap ability of restraining disturbances, and the given norm index is satisfied. Simulation results demonstrate that the proposed observer can detect the faults sensitively, and the influence of unknown disturbance on residual error can be restrained to a given range.