TY - JOUR
T1 - Constructing a homogeneous LTI descriptor system with desired properties using perturbation theory
AU - Pantelous, Athanasios A.
AU - Karageorgos, Athanasios D.
AU - Kalogeropoulos, Grigoris I.
PY - 2011/11/1
Y1 - 2011/11/1
N2 - In the literature regarding linear systems and mathematical control theory, several different techniques have been developed for obtaining the solution of homogeneous linear time-invariant (LTI) descriptor differential systems. In this article, applying the complex Weierstrass canonical form, we investigate the conditions under which a descriptor system with a specific structure and desired properties is being constructed using perturbation theory. Our approach is very general, and as an example, a stable homogeneous LTI descriptor system is designed. Thus, a proportional and derivative controller can be used, such as the case where a family of perturbed pencils is defined and the solutions of the initial and the relative perturbed systems are ρM(t)-close with respect to a Frobenius distance. A Step-algorithm and an illustrative example are also presented to illustrate the results of this article.
AB - In the literature regarding linear systems and mathematical control theory, several different techniques have been developed for obtaining the solution of homogeneous linear time-invariant (LTI) descriptor differential systems. In this article, applying the complex Weierstrass canonical form, we investigate the conditions under which a descriptor system with a specific structure and desired properties is being constructed using perturbation theory. Our approach is very general, and as an example, a stable homogeneous LTI descriptor system is designed. Thus, a proportional and derivative controller can be used, such as the case where a family of perturbed pencils is defined and the solutions of the initial and the relative perturbed systems are ρM(t)-close with respect to a Frobenius distance. A Step-algorithm and an illustrative example are also presented to illustrate the results of this article.
KW - linear descriptor systems
KW - matrix pencil theory
KW - perturbation theory
UR - http://www.scopus.com/inward/record.url?scp=84856726210&partnerID=8YFLogxK
U2 - 10.1080/00207179.2011.629322
DO - 10.1080/00207179.2011.629322
M3 - Article
AN - SCOPUS:84856726210
VL - 84
SP - 1915
EP - 1925
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 11
ER -