Application of the Drazin inverse of matrices to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor linear systems

Tadeusz Kaczorek

Abstract

The 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.
Author Tadeusz Kaczorek (FEE/DACR)
Tadeusz Kaczorek,,
- Department of Control Engineering and Electronics
Pages195-204
Publication size in sheets0.50
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 identifierROC 19-20
Languageen angielski
Score (nominal)20
Score sourcepublisherList
ScoreMinisterial score = 20.0, 01-04-2020, ChapterFromConference
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