Application of the Drazin inverse of matrices to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor linear systems
AbstractThe Drazin inverse of matrices is applied to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor linear continuous-time and discrete-time systems. It is shown that: 1) The descriptor linear continuous-time system is pointwise complete if and only if the initial and final states belong to the same subspace. 2) The descriptor linear discrete-time system is not pointwise complete if its system matrix is singular. 3) System obtained by discretisation of continuous-time system is always not pointwise complete. 4) The descriptor linear continuous-time system is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. Considerations are illustrated by example of descriptor linear electrical circuit.
|Publication size in sheets||0.5|
|Book||Awrejcewicz Jan, Kaźmierczak M., Mrozowski Jerzy (eds.): Theoretical Approaches in Non-Linear Dynamical Systems, vol. 1, 2019, Wydawnictwo Politechniki Łódzkiej, ISBN 978-83-66287-29-7, 576 p., DOI:10.34658/9788366287297|
|Internal identifier||ROC 19-20|
|Score||= 20.0, 01-04-2020, ChapterFromConference|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.