## Displaying similar documents to “A classification of generalised state space reduction methods for linear multivariable systems”

### On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems

International Journal of Applied Mathematics and Computer Science

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We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is...

### An equivalent matrix pencilfor bivariate polynomial matrices

International Journal of Applied Mathematics and Computer Science

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In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

Kybernetika

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### New coprime polynomial fraction representation of transfer function matrix

Kybernetika

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A new form of the coprime polynomial fraction $C\left(s\right)\phantom{\rule{0.166667em}{0ex}}F{\left(s\right)}^{-1}$ of a transfer function matrix $G\left(s\right)$ is presented where the polynomial matrices $C\left(s\right)$ and $F\left(s\right)$ have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices $HB$, $HAB$, ...

### Proper feedback compensators for a strictly proper plant by polynomial equations

International Journal of Applied Mathematics and Computer Science

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We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the...

### Equivalence and reduction of delay-differential systems

International Journal of Applied Mathematics and Computer Science

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A new direct method is presented which reduces a given high-order representation of a control system with delays to a first-order form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant...