Parity space-based fault detection for Markovian jump systems

Abstract

This article deals with problems of parity space-based fault detection for a class of discrete-time linear Markovian jump systems. A new algorithm is firstly introduced to reduce the computation of mode-dependent redundancy relation parameter matrices. Different from the case of linear time invariant systems, the parity space-based residual generator for a Markovian jump system cannot be designed off-line because it depends on the history of system modes in the last finite steps. In order to overcome this difficulty, a finite set of parity matrices is pre-designed applying a unified approach to linear time invariant systems. Then the on-line residual generation can be easily implemented. Moreover, the problem of residual evaluation is also considered which includes the determination of a residual evaluation function and a threshold. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords:

• fault detection
• Markovian jump system
• residual
• parity space
• threshold

Acknowledgements

The work was partially supported by the NSF of China (60774071, 60736025), the PhD Program Foundation of Education Ministry of China (20050422036) and the Grant of Shandong Province (2005BS01007).