In the chapter 2, the author introduce two methods that method a sign pattern matrix is spectrally arbitrary, the structure method and Nilpotent-Jacobi method with examples.

I analyse some conclusions of spectrum arbitrary and give two sign patterns. then I prove two classes sign pattern matrix that are spectrally arbitrary using Nilpotent-Jacobi method.

This method based on modified nodal approach is easy to set up the fault diagnosis equations and has lower degree of nonlinearity and regular Jacobi matrix form.