Decay of singular values of the Gramians of infinite-dimensional systems

Mark Opmeer

doi:10.1109/ECC.2015.7330700

Decay of singular values of the Gramians of infinite-dimensional systems

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

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Abstract

We show that the Gramians of a control system with an analytic semigroup, control and observation operators that are not too unbounded and which have finite-dimensional input and output spaces have singular values which decay exponentially in the square root. As a corollary it is shown that the Hankel singular values of such control systems also decay exponentially in the square root. Another corollary shows that solutions of algebraic Riccati equations for such systems also have singular values which decay exponentially in the square root.

Original language	English
Title of host publication	Proceedings of the 14th European Control Conference (ECC), 2015
Publisher	IEEE
Pages	1183-1188
DOIs	https://doi.org/10.1109/ECC.2015.7330700
Publication status	Published - 2015
Event	14th European Control Conference (ECC2015) - Linz, Austria Duration: 15 Jul 2015 → 17 Jul 2015

Conference

Conference	14th European Control Conference (ECC2015)
Country/Territory	Austria
City	Linz
Period	15/07/15 → 17/07/15

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10.1109/ECC.2015.7330700

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title = "Decay of singular values of the Gramians of infinite-dimensional systems",

abstract = "We show that the Gramians of a control system with an analytic semigroup, control and observation operators that are not too unbounded and which have finite-dimensional input and output spaces have singular values which decay exponentially in the square root. As a corollary it is shown that the Hankel singular values of such control systems also decay exponentially in the square root. Another corollary shows that solutions of algebraic Riccati equations for such systems also have singular values which decay exponentially in the square root.",

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AB - We show that the Gramians of a control system with an analytic semigroup, control and observation operators that are not too unbounded and which have finite-dimensional input and output spaces have singular values which decay exponentially in the square root. As a corollary it is shown that the Hankel singular values of such control systems also decay exponentially in the square root. Another corollary shows that solutions of algebraic Riccati equations for such systems also have singular values which decay exponentially in the square root.

UR - http://dx.doi.org/10.1109/ECC.2015.7330700

U2 - 10.1109/ECC.2015.7330700

DO - 10.1109/ECC.2015.7330700

M3 - Chapter in a published conference proceeding

SP - 1183

EP - 1188

BT - Proceedings of the 14th European Control Conference (ECC), 2015

PB - IEEE

T2 - 14th European Control Conference (ECC2015)

Y2 - 15 July 2015 through 17 July 2015

ER -

Decay of singular values of the Gramians of infinite-dimensional systems

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