Wyniki wyszukiwania - BazTech

1

Pointwise completeness and pointwise degeneracy of fractional standard and descriptor linear continuous-time systems with different fractional orders

Kaczorek Tadeusz, Sajewski Łukasz

International Journal of Applied Mathematics and Computer Science

|

2020

|

Vol. 30, no. 4

641--647

EN

Descriptor and standard linear continuous-time systems with different fractional orders are investigated. Descriptor systems are analyzed making use of the Drazin matrix inverse. Necessary and sufficient conditions for the pointwise completeness and pointwise degeneracy of descriptor continuous-time linear systems with different fractional orders are derived. It is shown that (i) the descriptor linear continuous-time system with different fractional orders is pointwise complete if and only if the initial and final states belong to the same subspace, (ii) the descriptor linear continuous-time system with different fractional orders is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. Results are reported for the case of two different fractional orders and can be extended to any number of orders.

2

Application of the Drazin inverse to the analysis of pointwise completeness and pointwise degeneracy of descriptor fractional linear continuous-time systems

Kaczorek Tadeusz, Ruszewski Andrzej

International Journal of Applied Mathematics and Computer Science

|

2020

|

Vol. 30, no. 2

219--223

EN

The Drazin inverse of matrices is applied to the analysis of pointwise completeness and pointwise degeneracy of fractional descriptor linear continuous-time systems. It is shown that (i) descriptor linear continuous-time systems are pointwise complete if and only if the initial and final states belong to the same subspace, and (ii) fractional descriptor linear continuous-time systems are not pointwise degenerated in any nonzero direction for all nonzero initial conditions. The discussion is illustrated with examples of descriptor linear electrical circuits.

3

Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

|

2015

|

Vol. 25, no. 2

217--221

EN

Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.

4

Punktowa zupełność i punktowa degeneracja dodatnich układów dyskretnych z opóźnieniami

Busłowicz M., Kociszewski R., Trzasko W.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

|

2006

|

z. 145

51-56

PL

W pracy sformułowano definicje oraz podano warunki konieczne i wystarczające punktowej zupełności oraz punktowej degeneracji dyskretnych dodatnich układów liniowych stacjonarnych z opóźnieniami zmiennych stanu. Podano też metodę wyznaczania warunków początkowych, dla których trajektoria stanu układu punktowo zupełnego przechodzi przez dowolny zadany nieujem-ny stan końcowy. Rozważania zilustrowano przykładem.

EN

Definitions and necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of positive discrete-time linear systems with delays have been given.