Fault detection for linear discrete time-varying systems with multiplicative noise based on parity space method

This paper addresses the robust fault diagnosis problem for a class of linear discrete time-varying systems with multiplicative noise based on parity space method. A novel fault detection performance index, in terms of stochastic robustness/sensitivity ratio, is proposed to establish the residual generator. A computationally attractive recursive algorithm, is put forward to obtain the complex matrix involved in the aforementioned fault detection performance index. Drawing support of random matrix analysis and calculation, the corresponding solution is derived in an analytical form via solving a multi-objective optimization problem. By means of Randomized Algorithms, two fault detection threshold setting algorithms are provided subsequently to achieve residual performance assessment by taking into account the fault detection rate and false alarm rate in the probabilistic framework. Two illustrative examples are finally provided to illustrate the effectiveness of the proposed scheme.