Minimal realizations of input-output behaviors by LPV state-space representations with affine dependency

M. Petreczky; Roland Tóth; Guillaume Mercere

Minimal realizations of input-output behaviors by LPV state-space representations with affine dependency

M. Petreczky, Roland Tóth, Guillaume Mercere

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Abstract

This letter makes the first steps towards a behavioral theory of LPV state-space representations with only affine dependence on the scheduling signal, by characterizing minimality of such state-space representations. We show that minimality is equivalent to observability, and that minimal realizations of the same behavior are isomorphic. Finally, we establish a formal relationship between minimality of LPV state-space representations with an affine dependence on the scheduling signal and minimality of LPV state-space representations with a dynamic and meromorphic dependence on the scheduling signal.

Original language	English
Publication status	Published - Dec 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023 Conference number: 62

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Abbreviated title	CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

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cdc2023Final author version , 264 KBLicence: CC BY-SA

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Minimal Realizations of Input-Output Behaviors by LPV State-Space Representations with Affine Dependence
Petreczky, M. (Corresponding author), Tóth, R. & Mercere, G., 2023, In: IEEE Control Systems Letters. 7, p. 2952-2957 6 p.
Research output: Contribution to journal › Article › Academic › peer-review

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title = "Minimal realizations of input-output behaviors by LPV state-space representations with affine dependency",

abstract = "This letter makes the first steps towards a behavioral theory of LPV state-space representations with only affine dependence on the scheduling signal, by characterizing minimality of such state-space representations. We show that minimality is equivalent to observability, and that minimal realizations of the same behavior are isomorphic. Finally, we establish a formal relationship between minimality of LPV state-space representations with an affine dependence on the scheduling signal and minimality of LPV state-space representations with a dynamic and meromorphic dependence on the scheduling signal.",

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AU - Mercere, Guillaume

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N2 - This letter makes the first steps towards a behavioral theory of LPV state-space representations with only affine dependence on the scheduling signal, by characterizing minimality of such state-space representations. We show that minimality is equivalent to observability, and that minimal realizations of the same behavior are isomorphic. Finally, we establish a formal relationship between minimality of LPV state-space representations with an affine dependence on the scheduling signal and minimality of LPV state-space representations with a dynamic and meromorphic dependence on the scheduling signal.

AB - This letter makes the first steps towards a behavioral theory of LPV state-space representations with only affine dependence on the scheduling signal, by characterizing minimality of such state-space representations. We show that minimality is equivalent to observability, and that minimal realizations of the same behavior are isomorphic. Finally, we establish a formal relationship between minimality of LPV state-space representations with an affine dependence on the scheduling signal and minimality of LPV state-space representations with a dynamic and meromorphic dependence on the scheduling signal.

M3 - Paper

T2 - 62nd IEEE Conference on Decision and Control, CDC 2023

Y2 - 13 December 2023 through 15 December 2023

ER -

Minimal realizations of input-output behaviors by LPV state-space representations with affine dependency

Abstract

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Minimal Realizations of Input-Output Behaviors by LPV State-Space Representations with Affine Dependence

Cite this