Kalman-Popov-Yakubovich lemma for ordered fields

Standard

Kalman-Popov-Yakubovich lemma for ordered fields. / Gusev, S.V.

In: Automation and Remote Control, No. 1, 2014, p. 18-33.

Research output: Contribution to journal › Article › peer-review

Author

Gusev, S.V. / Kalman-Popov-Yakubovich lemma for ordered fields. In: Automation and Remote Control. 2014 ; No. 1. pp. 18-33.

BibTeX

@article{87f94de92385426aa7948763fa1e2c9d,

title = "Kalman-Popov-Yakubovich lemma for ordered fields",

abstract = "The Kalman-Popov-Yakubovich lemma was generalized to the case where the field of scalars is an ordered field that possesses the following property: if each value of the polynomial of one variable is the sum of squares, then the polynomial itself is the sum of squares of polynomials. The field with this property was named the sum of squares (SOS) field. The SOS-fields are, for instance, those of rational numbers, algebraic numbers, real numbers, or rational fractions of several variables, with the coefficients from the aforementioned fields. It was proved that the statement of the Kalman-Popov-Yakubovich lemma about the equivalence of the frequency domain inequality and the linear matrix inequality holds true if the SOS-field is considered as a that of scalars. An example was presented which shows that in the SOS-field the fulfillment of the frequency domain inequality does not imply solvability of the corresponding algebraic Riccati equation. {\textcopyright} 2014 Pleiades Publishing, Ltd.",

author = "S.V. Gusev",

year = "2014",

doi = "10.1134/S0005117914010020",

language = "English",

pages = "18--33",

journal = "Automation and Remote Control",

issn = "0005-1179",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "1",

}

RIS

TY - JOUR

T1 - Kalman-Popov-Yakubovich lemma for ordered fields

AU - Gusev, S.V.

PY - 2014

Y1 - 2014

N2 - The Kalman-Popov-Yakubovich lemma was generalized to the case where the field of scalars is an ordered field that possesses the following property: if each value of the polynomial of one variable is the sum of squares, then the polynomial itself is the sum of squares of polynomials. The field with this property was named the sum of squares (SOS) field. The SOS-fields are, for instance, those of rational numbers, algebraic numbers, real numbers, or rational fractions of several variables, with the coefficients from the aforementioned fields. It was proved that the statement of the Kalman-Popov-Yakubovich lemma about the equivalence of the frequency domain inequality and the linear matrix inequality holds true if the SOS-field is considered as a that of scalars. An example was presented which shows that in the SOS-field the fulfillment of the frequency domain inequality does not imply solvability of the corresponding algebraic Riccati equation. © 2014 Pleiades Publishing, Ltd.

AB - The Kalman-Popov-Yakubovich lemma was generalized to the case where the field of scalars is an ordered field that possesses the following property: if each value of the polynomial of one variable is the sum of squares, then the polynomial itself is the sum of squares of polynomials. The field with this property was named the sum of squares (SOS) field. The SOS-fields are, for instance, those of rational numbers, algebraic numbers, real numbers, or rational fractions of several variables, with the coefficients from the aforementioned fields. It was proved that the statement of the Kalman-Popov-Yakubovich lemma about the equivalence of the frequency domain inequality and the linear matrix inequality holds true if the SOS-field is considered as a that of scalars. An example was presented which shows that in the SOS-field the fulfillment of the frequency domain inequality does not imply solvability of the corresponding algebraic Riccati equation. © 2014 Pleiades Publishing, Ltd.

U2 - 10.1134/S0005117914010020

DO - 10.1134/S0005117914010020

M3 - Article

SP - 18

EP - 33

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 1

ER -

ID: 7061302