Unstable Aircraft
Modern military aircraft and in particular low observable designs often exhibit instability as a result of their design. The Lockheed F-117 Nighthawk for instance employs a highly non-traditional fuselage and wing shape in order to reduce its radar cross section and enable it to penetrate air defences with relative impunity. However the flat facets of the design reduce its stability to the point where a digital fly-by-wire system was required to allow safe operation. The difficulty in flying such an aircraft without fly-by-wire can be illustrated by the proof-of-concept vehicle developed prior to the Nighthawk, Have Blue.
Though it is not just fighter jets that have relaxed stability designs. The McDonnell Douglas MD-11 has a relaxed stability design which was implemented to save fuel. To ensure stability for safe flight, an LSAS (longitudinal stability augmentation system) was introduced to compensate for the MD-11's rather short horizontal stabilizer to ensure that the aircraft would remain stable. However, there have been incidents in the past in which the MD-11's relaxed stability caused an "inflight upset."
Read more about this topic: Relaxed Stability