General transformation for block diagonalization of weakly coupled linear systems composed of N-subsystems

A transformation is introduced for exact decomposition (block-diagonalization) of linear weakly coupled systems composed of N subsystems. This transformation can also be used for block diagonalization of block-diagonally dominant matrices and, under certain assumptions, it can be applied for block diagonalization of nearly completely decomposable Markov chains. A twelfth-order real-world power system example is included to demonstrate the efficiency of the proposed method.