Finite-frequency fault detection based on derandomisation for Markov jump linear system

The fault detection filter design for Markov jump linear system (MJLS) in finite-frequency domain based on derandomisation is proposed in this study. By means of generalised Kalman–Yakubovich–Popov (GKYP) lemma, the finite-frequency fault detection problem for deterministic systems can be easily solved. However, MJLS is a multi-mode system jumping among different modes stochastically. Consequently, its performance in finite-frequency domain cannot be directly achieved by GKYP lemma. Therefore, the derandomisation technique is introduced to transform stochastic multi-mode systems to deterministic single-mode systems. Then based on the transformed deterministic system, a fault detection filter for MJLS with both fault and noise in specific frequency ranges is designed. To demonstrate the superiority of the authors' theoretical results, a numerical example and a real application with engineering background are presented.