A note on mode decoupling of linear time-invariant systems using the generalized sign matrix

It is shown how to decouple a selected set of modes of linear-time invariant systems. The decoupling procedure is based on a spectral decomposition of the system matrix using the generalized sign function. This decomposition does not require knowledge of eigenvalues and eigenvectors. The resulting projectors act as decoupling matrices for a spectral domain of the solution. This decomposition is particularly useful in linear time-invariant system equations. The computational procedure is given within.