A New Interval Observer Design Method with Application to Fault Detection

Abstract

This chapter proposes a novel interval observer for continuous-time linear systems with unknown disturbance. Based on the stability criterion of a Metzler matrix, the interval observer design problem is converted into a series of nonlinear inequalities. To attenuate the effect of unknown disturbance on estimation error, an interval observer design method based on constrained optimization is proposed. The proposed interval observer is able to estimate upper and lower bounds of the states in the general assumption that disturbance is unknown but bounded. Thus it is particularly suitable for fault detection for uncertain linear systems. Therefore, the proposed method is further used to generate dynamic thresholds to achieve fault detection. Finally, a flight control system is simulated to demonstrate the effectiveness of the proposed method.