On the Zero-Freeness of Tall Multirate Linear Systems

In this technical note, tall discrete-time linear systems with multirate outputs are studied. In particular, we focus on their zeros. In systems and control literature zeros of multirate systems are defined as those of their corresponding time-invariant systems obtained through blocking of the origi...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 61; no. 11; pp. 3606 - 3611
Main Authors Zamani, Mohsen, Bottegal, Giulio, Anderson, Brian D. O.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.11.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Australia
Biological system modeling
Control systems
Delay
Discrete time systems
Econometrics
Filtering theory
Infinity
Linear systems
Mathematical analysis
Matrices (mathematics)
MIMO
multirate
Origins
Transfer functions
zero-freeness
zeros
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Summary:In this technical note, tall discrete-time linear systems with multirate outputs are studied. In particular, we focus on their zeros. In systems and control literature zeros of multirate systems are defined as those of their corresponding time-invariant systems obtained through blocking of the original multirate systems. We assume that blocked systems are tall, i.e., have more outputs than inputs. It is demonstrated that, for generic choice of the parameter matrices, linear systems with multirate outputs generically have no finite nonzero zeros. However, they may have zeros at the origin or at infinity depending on the choice of blocking delay and the input, state and output dimensions.
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content type line 23
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2016.2527924