Disturbance decoupling in fault detection of linear periodic systems

This paper studies fault detection problems of linear discrete-time periodic systems. The aim is to design residual generators, which deliver a residual signal fully decoupled from unknown disturbances. First, a periodic parity relation based full decoupling residual generator with a periodically varying parity vector is established. Then, the relation between periodic parity vectors and periodic observer-based residual generators is investigated. It is shown that a periodic observer-based full decoupling residual generator can be obtained from a periodic full decoupling parity vector. Finally, the condition of disturbance decoupling is discussed and an example is given to illustrate the proposed approaches.