Characterization of the minimum detectable fault of interval observers by using set-invariance theory

This paper addresses the characterization of the minimum detectable fault when using interval observers. The interval observers consider both input and uncertainty as unknown but bounded. The minimum detectable fault using interval observers is characterized by means of residual sensitivity and invariant sets. The design of such observers is performed by using zonotopic-set representations. The mathematical expression of the minimum magnitude of the fault that can be detected is derived for a given type of faults in separate formulations. Finally, a simulation example is employed to illustrate and discuss the effectiveness of the obtained results.