Robust Sensor Faults Reconstruction for a Class of Uncertain Linear Systems Using a Sliding Mode Observer: An LMI Approach

This paper presents a design method of a Sliding Mode Observer (SMO) for robust sensor faults reconstruction of systems with matched uncertainty. This class of uncertainty requires a known upper bound. The basic idea is to use the H_∞ concept to design the observer, which minimizes the effect of the uncertainty on the reconstruction of the sensor faults. Specifically, we applied the equivalent output error injection concept from previous work in Fault Detection and Isolation (FDI) scheme. Then, these two problems of design and reconstruction can be expressed and numerically formulate via Linear Matrix Inequalities (LMIs) optimization. Finally, a numerical example is given to illustrate the validity and the applicability of the proposed approach.