本文研究一类具有随机时变时滞及随机发生非线性(RONs)的离散时间马尔可夫跳跃系统的故障检测问题。针对多重时变时滞发生时所具有的随机特性，使用相互独立的伯努利随机过程来刻画这一现象。进一步地，在故障检测研究中考虑一类由伯努利分布白序列描述的随机非线性干扰。本文的目的是设计一个故障检测滤波器，使得整个误差动态系统满足均方指数稳定及相应的H∞性能指标。通过Lyapunov稳定性理论及随机分析技术，建立满足均方指数稳定和H∞干扰抑制的充分条件，进而使用半定程序方法求解一个凸优化问题，获取所设计的故障检测滤波器增益特性。最后，通过仿真算例证实了该设计方法的实用性和有效性。%This paper is concerned with the fault detection problem for a class of discrete-time Markovian jump systems with multiple time-varying stochastic delays and randomly occurring nonlinearities. According to the stochastic character-istic of multiple time-varying delays, an individual Bernoulli distribution is used to describe this phenomenon. Furthermore, a kind of stochastic nonlinear disturbance is also considered in the fault detection research by means of a Bernoulli dis-tributed white sequence. The main purpose of this paper is to design a fault detection filter such that the residual system is mean square exponential stable and the relevant H∞ performance is satisfied. Through Lyapunov stability theory and stochastic analysis technology, sufficient conditions are set up for the desired exponential stability and H∞ disturbance attenuation, a convex optimization problem is solved by the semidefinite programming technique, the gain characteristic of the fault detection filter is obtained. Finally, a simulation example is provided to illustrate the usefulness and effectiveness of the proposed design approach.
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