Modification of Infinite and Unstable Invariant Zeros in Linear Systems Using Stability-Preserving State Feedback

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F24%3A00377633" target="_blank" >RIV/68407700:21730/24:00377633 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1109/TAC.2024.3394129" target="_blank" >https://doi.org/10.1109/TAC.2024.3394129</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TAC.2024.3394129" target="_blank" >10.1109/TAC.2024.3394129</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Modification of Infinite and Unstable Invariant Zeros in Linear Systems Using Stability-Preserving State Feedback

Popis výsledku v původním jazyce

The algebra of integral matrices is applied to solve the following problem of control theory: modification of a specified list of zeros of a linear system with more inputs than outputs using nonregular state feedback while ensuring stability or, equivalently, the modification of a specified list of zeros of a stable system while maintaining stability. The zeros in question are unstable invariant zeros and the zero at infinity. These zeros are the Smith invariant of the transfer matrix of the given stable system, which is a proper and stable rational matrix. Since the action of any stability-preserving state feedback can be represented by the multiplication of the system transfer matrix on the right by a proper and stable rational matrix, called a cascade compensator, the study of the control problem amounts to the study of Smith invariants of a product of two integral matrices. However, only cascade compensators that can be implemented using state feedback are of interest. This is why the solvability conditions depend on the system's column-minimal indices. It turns out that existing infinite and unstable invariant zeros cannot be displaced; only their multiplicity can be increased, and new zeros can be created. Typical applications include stable model matching and stable decoupling by state feedback.

Název v anglickém jazyce

Modification of Infinite and Unstable Invariant Zeros in Linear Systems Using Stability-Preserving State Feedback

Popis výsledku anglicky

The algebra of integral matrices is applied to solve the following problem of control theory: modification of a specified list of zeros of a linear system with more inputs than outputs using nonregular state feedback while ensuring stability or, equivalently, the modification of a specified list of zeros of a stable system while maintaining stability. The zeros in question are unstable invariant zeros and the zero at infinity. These zeros are the Smith invariant of the transfer matrix of the given stable system, which is a proper and stable rational matrix. Since the action of any stability-preserving state feedback can be represented by the multiplication of the system transfer matrix on the right by a proper and stable rational matrix, called a cascade compensator, the study of the control problem amounts to the study of Smith invariants of a product of two integral matrices. However, only cascade compensators that can be implemented using state feedback are of interest. This is why the solvability conditions depend on the system's column-minimal indices. It turns out that existing infinite and unstable invariant zeros cannot be displaced; only their multiplicity can be increased, and new zeros can be created. Typical applications include stable model matching and stable decoupling by state feedback.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotika a pokročilá průmyslová výroba</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Transactions on Automatic Control

ISSN

0018-9286

e-ISSN

1558-2523

Svazek periodika

69

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

8

Strana od-do

7166-7173

Kód UT WoS článku

001322635200030

EID výsledku v databázi Scopus

2-s2.0-85192138972