Robust Fault Detection for Switched Systems based on Interval Observers

This paper deals with fault detection (FD) for a class of discrete-time switched systems with sensor faults. Under the assumption that disturbances and measurement noise are unknown but bounded, two methods, respectively based on the $H_{\infty}$ and the $L_{\infty}$ formalisms, are introduced to attenuate the effects of the uncertainties and to improve the accuracy of the proposed residual framers. The design conditions of the interval observer are given in terms of Linear Matrix Inequalities (LMIs). Furthermore, a FD decision is developed to indicate the presence of faults. A numerical example is performed to illustrate the effectiveness of the proposed method based on the $L_{\infty}$ performance through a comparison with the results obtained using the $H_{\infty}$ analysis.