An interesting class of feedback matrices, also explored by Jot , is that of triangular matrices. A basic fact from linear algebra is that triangular matrices (either lower or upper triangular) have all of their eigenvalues along the diagonal.4.13 For example, the matrix
It is important to note that not all triangular matrices are lossless. For example, consider
One way to avoid ``coupled repeated poles'' of this nature is to use non-repeating eigenvalues. Another is to convert to Jordan canonical form by means of a similarity transformation, zero any off-diagonal elements, and transform back .
Mean Free Path
Most General Lossless Feedback Matrices