Abstract
In this paper, we propose a new approach for the analysis and design of sliding-mode observer (SMO) under some matching conditions for a class of for a class of linear uncertain systems. We derive existence conditions sliding mode observers in terms of constrained Linear Matrix Inequalities (LMIs) guaranteeing a stable sliding motion on the switching surface. The gain matrices of the sliding-mode observer are characterized using the solution of the LMI existence condition. The generation of sliding modes permits the reconstruction of faults using the equivalent output injection which based on the available plant input/output information and can be calculated with on-line method. A scale crane example taken from the fault detection literature is used to demonstrate the method and its effectiveness.