![](/images/graphics-bg.png)
On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays
Author
Source
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-34, 34 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-08-20
Country of Publication
Egypt
No. of Pages
34
Main Subjects
Abstract EN
This paper investigates the causality properties of a class of linear time-delay systems under constant point delays which possess a finite set of distinct linear time-invariant parameterizations (or configurations) which, together with some switching function, conform a linear time-varying switched dynamic system.
Explicit expressions are given to define pointwisely the causal and anticausal Toeplitz and Hankel operators from the set of switching time instants generated from the switching function.
The case of the auxiliary unforced system defined by the matrix of undelayed dynamics being dichotomic (i.e., it has no eigenvalue on the complex imaginary axis) is considered in detail.
Stability conditions as well as dual instability ones are discussed for this case which guarantee that the whole system is either stable, or unstable but no configuration of the switched system has eigenvalues within some vertical strip including the imaginary axis.
It is proved that if the system is causal and uniformly controllable and observable, then it is globally asymptotically Lyapunov stable independent of the delays, that is, for any possibly values of such delays, provided that a minimum residence time in-between consecutive switches is kept or if all the set of matrices describing the auxiliary unforced delay—free system parameterizations commute pairwise.
American Psychological Association (APA)
de La Sen, Manuel. 2009. On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays. Abstract and Applied Analysis،Vol. 2009, no. 2009, pp.1-34.
https://search.emarefa.net/detail/BIM-489095
Modern Language Association (MLA)
de La Sen, Manuel. On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays. Abstract and Applied Analysis No. 2009 (2009), pp.1-34.
https://search.emarefa.net/detail/BIM-489095
American Medical Association (AMA)
de La Sen, Manuel. On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays. Abstract and Applied Analysis. 2009. Vol. 2009, no. 2009, pp.1-34.
https://search.emarefa.net/detail/BIM-489095
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-489095