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Characteristics of LTI descriptor systems
Author(s) -
Müller Peter C.
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110404
Subject(s) - equivalence (formal languages) , lti system theory , transformation (genetics) , mathematics , rank (graph theory) , invariant (physics) , matrix (chemical analysis) , transformation matrix , pure mathematics , transfer (computing) , control theory (sociology) , linear system , combinatorics , computer science , mathematical analysis , control (management) , physics , chemistry , biochemistry , kinematics , chromatography , classical mechanics , artificial intelligence , parallel computing , mathematical physics , gene
Abstract Linear time‐invariant (LTI) descriptor systems Eẋ = Ax + Bu with regular matrix pencils λ( E − A ) may be separated by an equivalence transformation into a “slow” and a “fast” subsystem. The consistent solution of the fast subsystem can be presented by the input u and its time‐derivatives. If these time‐derivatives appear explicitly, then the system behaviour is called improper, otherwise it is proper or even strictly proper. This contribution deals with the determination of the related characteristics based on the matrices E , A , B without applying the equivalence transformation: Index k, orders n1, n2 of the subsystems ( n 1 + n 2 = n ), (strictly) proper and improper transfer behaviour, degree of improperness of each individual input. These characteristics are calculated by rank conditions of suitable matrices composed of E , A , B . (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)