Abstarct: Today modern dynamic systems have become very complex. However occurring a fault in this systems is unavoidable. Fault can cause serious damage and make systems to become totally failure. For this reason the Fault detection system is a first step for fault tolerant system.The presence of model uncertainty , disturbance and noises is a main problem in fault detection systems.Purpose in fault detection systems is provide a residual signal such that eliminate unwanted signals from that and influence fault in residual signal.For handed to this purpose we use Observers for many Advantage of them.In this thesis an optimal solution H_ /H∞ to the problem of Fault detection in non-linear time invariant system is presented . designed for F16 aircraft and simulated and design observer for F16 and at the end compare this observer with the other famous observers in fault detection .then the results are in chapter 5 .