Opuscula Math. 37, no. 1 (2017), 21-64

Opuscula Mathematica

The LQ/KYP problem for infinite-dimensional systems

Piotr Grabowski

Abstract. Our aim is to present a solution to a general linear-quadratic (LQ) problem as well as to a Kalman-Yacubovich-Popov (KYP) problem for infinite-dimensional systems with bounded operators. The results are then applied, via the reciprocal system approach, to the question of solvability of some Lur'e resolving equations arising in the stability theory of infinite-dimensional systems in factor form with unbounded control and observation operators. To be more precise the Lur'e resolving equations determine a Lyapunov functional candidate for some closed-loop feedback systems on the base of some properties of an uncontrolled (open-loop) system. Our results are illustrated in details by an example of a temperature of a rod stabilization automatic control system.

Keywords: control of infinite-dimensional systems, semigroups, infinite-time LQ-control problem, Lur'e feedback systems.

Mathematics Subject Classification: 49N10, 93B05, 93C25.

Full text (pdf)

Opuscula Mathematica - cover

Cite this article as:
Piotr Grabowski, The LQ/KYP problem for infinite-dimensional systems, Opuscula Math. 37, no. 1 (2017), 21-64, http://dx.doi.org/10.7494/OpMath.2017.37.1.21

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.