Block-diagonal dominant canonical form via singular value decomposition

Singular value decomposition is used to determine certain parity-orthogonal and orthogonal transformations to obtain a 'Block-diagonal dominant' canonical form of the system model. The canonical form is useful in the partitioning of a large scale system, and is always obtainable when the spectrum of the system matrix is separable into distinct groups relative to the modulus of the eigenvalues-a usual case in control systems. The procedure avoids the use of eigenstructure routines which are not helpful for ill-conditioned matrices. The parity-orthogonal transformations share some properties of orthogonal matrices; the inverse is obtainable from the transpose. The transformations and the procedure are demonstrated by an example. The orthogonal transformations-as opposed to parity-orthogonal transformations-appear relatively efficient for obtaining the canonical form. The transformations and the canonical form are not available in the literature; this is the original contribution of the paper.