The Degree of a Rational Matrix Function

1963 ◽  
Vol 11 (3) ◽  
pp. 645-658 ◽  
Author(s):  
R. J. Duffin ◽  
D. Hazony
Keyword(s):  
Matrix Function ◽  
Rational Matrix ◽  
Rational Matrix Function

scholarly journals Symmetric spectral factorisation of self-adjoint rational matrix functions

1997 ◽  
Vol 56 (1) ◽  
pp. 95-107
Author(s):  
G.J. Groenewald ◽  
M.A. Petersen
Keyword(s):  
Matrix Function ◽  
Matrix Functions ◽  
Rational Matrix ◽  
The Right ◽  
The Given ◽  
Rational Matrix Function ◽  
Spectral Factor

For a self-adjoint rational matrix function, not necessarily analytic at infinity, the existence of a right (symmetric) spectral factorisation is described in terms of a given left spectral factorisation. The formula for the right spectral factor is given in terms of the formula for the given left spectral factor. All formulas are based on a special realisation of a rational matrix function, which is different from ones that have been used before.

scholarly journals The continous kernel of a nonsquare rational matrix function

1992 ◽  
Vol 172 ◽  
pp. 85-96
Author(s):  
Richard E. Faulkenberry
Keyword(s):  
Matrix Function ◽  
Rational Matrix ◽  
Rational Matrix Function

Approximation of Irrational Matrix Functions and Its Application to Continuous-Discrete Model Conversion

1989 ◽  
Vol 111 (2) ◽  
pp. 142-145 ◽  
Author(s):  
Muh-Yang Chen ◽  
Chyi Hwang
Keyword(s):  
Matrix Function ◽  
Discrete Model ◽  
Matrix Functions ◽  
Rational Matrix ◽  
Improved Method ◽  
Matrix Logarithm ◽  
The Matrix ◽  
Model Conversion ◽  
Irrational Function ◽  
Rational Matrix Function

In this paper, an improved method of rational approximation is presented for evaluating the irrational matrix function f(A), where A is a square matrix and f(s) is a scalar irrational function which is analytic on the spectrum of A. The improvement in the accuracy of the approximation off (A) by a rational matrix function is achieved by using the multipoint Pade approximants to f(s). An application example to model conversion involving the evaluations of the matrix exponential exp (AT) and the matrix logarithm ln(F) is provided to illustrate the superiority of the method.

scholarly journals Generalized Fiedler pencils with repetition for rational matrix functions

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3529-3552
Author(s):  
Namita Behera
Keyword(s):  
Matrix Function ◽  
Linear Time ◽  
Matrix Functions ◽  
Rational Matrix ◽  
System Matrix ◽  
Space System ◽  
Linear Time Invariant ◽  
State Space System ◽  
Time Invariant ◽  
Rational Matrix Function

We introduce generalized Fiedler pencil with repetition(GFPR) for an n x n rational matrix function G(?) relative to a realization of G(?). We show that a GFPR is a linearization of G(?) when the realization of G(?) is minimal and describe recovery of eigenvectors of G(?) from those of the GFPRs. In fact, we show that a GFPR allows operation-free recovery of eigenvectors of G(?). We describe construction of a symmetric GFPR when G(?) is symmetric. We also construct GFPR for the Rosenbrock system matrix S(?) associated with an linear time-invariant (LTI) state-space system and show that the GFPR are Rosenbrock linearizations of S(?). We also describe recovery of eigenvectors of S(?) from those of the GFPR for S(?). Finally, We analyze operation-free Symmetric/self-adjoint structure Fiedler pencils of system matrix S(?) and rational matrix G(?). We show that structure pencils are linearizations of G(?).

Dynamic Stability Analysis by Matrix Function

1987 ◽  
Vol 113 (7) ◽  
pp. 1085-1100 ◽  
Author(s):  
Tsunemi Shigematsu ◽  
Takashi Hara ◽  
Mitao Ohga
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Matrix Function

scholarly journals Stability and McMillan degree for rational matrix interpolants

1994 ◽  
Vol 196 ◽  
pp. 207-232 ◽  
Author(s):  
Joseph A. Ball ◽  
Jeongook Kim
Keyword(s):  
Rational Matrix

scholarly journals Spectral properties of rational matrix functions with nonnegative realizations

1998 ◽  
Vol 275-276 ◽  
pp. 189-200 ◽  
Author(s):  
K.-H. Förster ◽  
B. Nagy
Keyword(s):  
Spectral Properties ◽  
Matrix Functions ◽  
Rational Matrix
Sign in / Sign up

Export Citation Format

Share Document