The descriptor system has the state equation \(E\dot x=Ax+Bu+Fw\) and the output equation \(y=Cx+Gw\), where \(\text{rank }E<n\) and \(w\) is an unmeasured input vector. The authors present a systematic observer design method based on the constrained Sylvester equation. Existence conditions are given. A nontrivial example is presented.