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The paper discusses the design of a robust fault detection system for linear discrete-time invariant uncertain systems. The intended system consists of norm-bounded uncertainty, stochastic uncertainty, and external unknown input. Due to the mixed uncertainties,  H∞  based model matching technique is used to develop a robust system that offers maximum sensitivity to faults and minimum sensitivity to all other unknown inputs. Reference residual model is designed using co-inner-outer factorization and the fault detection system is designed so that the error between reference residual and robust residual generated by fault detection filter (FDF) is minimized in  H∞  sense. The existing condition of FDF is exploited in terms of linear matrix inequalities. A numerical example and a benchmark three-tank system are simulated to illustrate the performance of the proposed fault detection system. Results confirm the effectiveness of the proposed approach by timely detecting the occurrence of the fault.

Model matching fault detection filter design for a linear discrete-time system with mixed uncertainties