Assignment of infinite zero orders in linear systems using state feedback

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F22%3A00353763" target="_blank" >RIV/68407700:21730/22:00353763 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.automatica.2021.109954" target="_blank" >https://doi.org/10.1016/j.automatica.2021.109954</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.automatica.2021.109954" target="_blank" >10.1016/j.automatica.2021.109954</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Assignment of infinite zero orders in linear systems using state feedback

Popis výsledku v původním jazyce

The problem of modifying the infinite zero orders in linear multivariable systems by nonregular state feedback is revisited. An entirely different algebraic approach is presented that offers new, inspiring insights into the problem. The approach is based on the properties of the invariant factors of a product of two proper rational matrices. A complete and explicit solution to the problem is established for linear multivariable systems described by quadruples (A, B, C, D). The system is first brought to Morse normal form so that one can identify the structural invariants and construct a state-feedback realizable compensator that assigns the prespecified infinite zero orders, then one returns to the original coordinates. The solvability condition, necessary and sufficient, is stated by using the system’s structural invariants; the use of conjugate lists of invariants is avoided. In addition to determining all infinite zero orders that can be assigned, the most important result of the new approach is a characterization of the structural properties of all compensators achieving every single assignable list of infinite zero orders. It turns out that this is a combinatorial problem. The solution set has the structure of a lattice of lists of nonnegative integers with a given sum, partially ordered by majorization.

Název v anglickém jazyce

Assignment of infinite zero orders in linear systems using state feedback

Popis výsledku anglicky

The problem of modifying the infinite zero orders in linear multivariable systems by nonregular state feedback is revisited. An entirely different algebraic approach is presented that offers new, inspiring insights into the problem. The approach is based on the properties of the invariant factors of a product of two proper rational matrices. A complete and explicit solution to the problem is established for linear multivariable systems described by quadruples (A, B, C, D). The system is first brought to Morse normal form so that one can identify the structural invariants and construct a state-feedback realizable compensator that assigns the prespecified infinite zero orders, then one returns to the original coordinates. The solvability condition, necessary and sufficient, is stated by using the system’s structural invariants; the use of conjugate lists of invariants is avoided. In addition to determining all infinite zero orders that can be assigned, the most important result of the new approach is a characterization of the structural properties of all compensators achieving every single assignable list of infinite zero orders. It turns out that this is a combinatorial problem. The solution set has the structure of a lattice of lists of nonnegative integers with a given sum, partially ordered by majorization.

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/EF15_003%2F0000466" target="_blank" >EF15_003/0000466: Umělá inteligence a uvažování</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Automatica

ISSN

0005-1098

e-ISSN

1873-2836

Svazek periodika

135

Číslo periodika v rámci svazku

January

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

—

Kód UT WoS článku

000716813000022

EID výsledku v databázi Scopus

2-s2.0-85117567254