Past information-based fault detection interval observer design for discrete-time systems

In this paper, a past information-based fault detection (FD) interval observer is designed for linear time-invariant discrete-time system with external disturbances. The past outputs, upper and lower estimations in a finite time window are applied to construct observer. Design freedom of the FD observer is raised by introducing the gain matrices of past information. The interval property is realized through time-delay positive systems theory and the undetermined observer matrices is solved with disturbance attenuation, fault sensitivity and nonnegativity conditions. The decision is implemented by residual interval and natural threshold. Finally, simulation is proceeded to declare the FD performance.