Title :
Linear algebraic properties of the realization matrix with applications to principal axis realizations
Author :
Maskarinec, Gregory J. ; Chitrapu, Prabhakar Rao
Author_Institution :
Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA, USA
fDate :
8/1/1992 12:00:00 AM
Abstract :
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 LΩ-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
Keywords :
discrete time systems; eigenvalues and eigenfunctions; frequency response; linear systems; matrix algebra; state-space methods; eigenvalues; frequency response; linear shift-invariant discrete-time system; minimality; principal axis realizations; qr-factorizations; realization matrix; singular values; spectral norm; state variable model; Digital filters; Eigenvalues and eigenfunctions; Frequency response; Helium; Linear matrix inequalities; Logic; Numerical analysis; Polynomials; Testing; Transfer functions;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
