Linear algebraic properties of the realization matrix with applications to principal axis realizations

摘要

Examines the realization matrix R=(A b; c d) defined by a state variable model of a linear, shift invariant, discrete time, scalar system. Several properties concerning the eigenvalues and singular values are derived, which are used to obtain tests for the minimality of the state variable model. An inequality is derived between the spectral norm of R and the L/sub Omega /-norm of its frequency response. The realization matrices of principal axis realizations are characterized in terms of their eigenvalues and singular values. qr-factorizations and bounds for the spectral norms of such realization matrices are derived.