Fault detection filter design for stochastic time-delay systems with sensor faults

Abstract

This article considers the fault detection (FD) problem for a class of Itô-type stochastic time-delay systems subject to external disturbances and sensor faults. The main objective is to design a fault detection filter (FDF) such that it has prescribed levels of disturbance attenuation and fault sensitivity. Sufficient conditions for guaranteeing these levels are formulated in terms of linear matrix inequalities (LMIs), and the corresponding fault detection filter design is cast into a convex optimisation problem which can be efficiently handled by using standard numerical algorithms. In order to reduce the conservatism of filter design with mixed objectives, multi-Lyapunov functions approach is used via Projection Lemma. In addition, it is shown that our results not only include some previous conditions characterising H _∞ performance and H ₋ performance defined for linear time-invariant (LTI) systems as special cases but also improve these conditions. Finally, two examples are employed to illustrate the effectiveness of the proposed design scheme.

Keywords:

• fault detection
• sensor fault
• stochastic time-delay systems
• fault sensitivity

Acknowledgements

This work was supported in part by the Funds for Creative Research Groups of China (No. 60821063), National 973 Program of China (Grant No. 2009CB320604), the Funds of National Science of China (Grant No. 60974043, 60904010), the 111 Project (B08015) and the Fundamental Research Funds for the Central Universities (No. N090604001).