Transfer function matrix and fundamental matrix of linear singular-descriptive systems
Dragutin Lj. Debeljković, PhD
Mića B. Jovanović, PhD
Ljubomir A. Jacić, PhD
The transfer matrix function has a particular significance in dynamical analysis
of real
linear singular multivariable feedback control systems from the stand point
of input – output realations, under the zero conditions. Natural connection with
fequency domain is obvious, necesary and therefore present in numerous methodes
and approaches. Several algorithms which allow the computation of transfer
function matrix of linear regular singular systems from the state space
description without inverting a polynomial matrix are presented. An allternative
closed-form expression for transfer function matrix in terms of matrix pencil
is
also given. Some of the approaches presented are direct extenssions of
Leverrier`s algorithm and some are its modifications.
A several numerical examples have been worked out to illustrate the methods
presented.
Fundamental matrix has a particular significance in dynamical analysis of real
linear discrete descriptive multivariable feedback control systems. This
paper shows that the forward and backward fundamental matrix sequence of regular
discrete descriptor system can be efficently used for computational purposes for
finding its state space transient response. Moreover, for such methods there is
no need to use Drazin or some other pseudo inversion procedures and Laurent
series expanssion is enough for these purposes.
Key words: linear systems, singular systems, descriptive systems, transfer function matrix, fundamental matrix.