Robust realizations and transformations

In the analysis and design of control systems, various algorithms employ well-conditioned similarity transformations, such as unitary and Householder transformations. The solution is then the exact solution of a nearby model. In this paper, an alternative well-conditioned and robust similarity transformation-to transform a matrix (in companion form) to a parity-normal matrix, is developed. The transformed matrix is robust with parity-normal eigenvectors. The developed similarity transformation is not available in the literature. It is anticipated that the transformation will prove very helpful in the design of well-conditioned algorithms for control system