  This work addresses the design of a robust hybrid observer for discrete-time
switched linear systems subject to unknown inputs and modeling errors. The
observer herein proposed is synthesized, for the case when the active mode is
unknown and in the purpose of robust fault detection. We'll show that a
suitable trade-off between the robustness to unknown inputs and sensitivity to
faults can be obtained through a performance index. The latter is optimized
using an iterative LMI solution procedure. The efficiency of the proposed
approach is illustrated by a numerical example.Keywords: Switched Systems,
Fault Detection, Observer design, optimization, Linear Matrix Inequality (LMI)
