The problem of output stabilization is studied for a class of linear hybrid systems subject to signal uncertainties: linear impulsive systems under dwell-time constraints. Two problems are considered. First, an interval observer estimating the set of admissible values for the state is designed. Next, an output stabilizing feedback design problem is studied where the stability is checked using linear matrix inequalities (LMIs). To the best of our knowledge, interval observer approach has never been proposed for the stabilization of this class of hybrid systems. Efficiency of the proposed approach is demonstrated by computer experiments for Fault Detection and Isolation (FDI) and Fault-Tolerant Control (FTC) of a power split device with clutch for heavy-duty military vehicles.