On the structure of balanced and other principal representations of SISO systems

A new matrix Wcowhich can be considered as a cross-Gramian matrix which contains information about both controllability and observability is defined for single-input, single-output, linear systems. Using this matrix, the structural properties of linear systems are studied in the context of principal component analysis. The matrix Wcocan be used in obtaining balanced and other principal representations without computation of the controllability and the observability Gramians. The importance of this matrix in model-order reduction is highlighted.