转移概率部分未知的正Markov切换系统的故障检测

Fault detection for positive Markov switching systems with partly unknown transition rates

研究了一类转移概率部分未知的正Markov切换系统的故障检测问题.通过选择模态相关的故障检测滤波器作为残差发生器,相应的故障检测被描述为正L_(1)滤波器问题.重点在于设计模态相关的故障检测滤波器,使得残差信号和故障信号之间的误差最小.然后,基于线性余正Lyapunov函数,在给定L_(1)增益性能指标下,建立了实现闭环系统期望随机稳定性的充分条件.进一步,线性规划方法建立了期望模态相关故障检测滤波器的可解性条件.最后,数值仿真验证了本方法的有效性.

This paper deals with the fault detection for Markov switching systems subject to positive constraint and partly unknown transition rates.By choosing a mode-dependent fault detection filter as a residual generator,the corresponding fault detection is formulated as a positive L_(1) filter problem.Attention is focused on the design of a mode-dependent fault detection filter to minimize the error between the residual signal and the fault signal.Subsequently,by means of the linear copositive Lyapunov function,sufficient conditions are proposed to achieve expected stochastic stability with a prescribed L_(1)-gain performance index.Some solvability conditions for the desired mode-dependent fault detection filter are established with the help of linear programming approach.Finally,a numerical simulation is given to demonstrate the validity of the main results.