Stability of linear equations with differentiable operators in a hilbert space

Michael Gil

doi:10.1093/imamci/dny035

Stability of linear equations with differentiable operators in a hilbert space

Michael Gil

Department of Mathematics

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

3 Scopus citations

Abstract

We consider the equation $\textrm{d}u(t)/\textrm{d}t=A(t)u(t)$ with an unbounded operator $A(t)$ in a Hilbert space having a bounded strong derivative. We derive the exponential and $L^2$ stability conditions. An illustrative example is presented.

Original language	English
Pages (from-to)	19-26
Number of pages	8
Journal	IMA Journal of Mathematical Control and Information
Volume	37
Issue number	1
DOIs	https://doi.org/10.1093/imamci/dny035
State	Published - 9 Mar 2020

Keywords

differential equation in a Hilbert space
linear non-autonomous equation
stability

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Applied Mathematics

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10.1093/imamci/dny035

Cite this

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title = "Stability of linear equations with differentiable operators in a hilbert space",

abstract = "We consider the equation \$\textbackslash{}textrm\{d\}u(t)/\textbackslash{}textrm\{d\}t=A(t)u(t)\$ with an unbounded operator \$A(t)\$ in a Hilbert space having a bounded strong derivative. We derive the exponential and \$L\textasciicircum{}2\$ stability conditions. An illustrative example is presented.",

keywords = "differential equation in a Hilbert space, linear non-autonomous equation, stability",

author = "Michael Gil",

note = "Publisher Copyright: {\textcopyright} 2018 Crown 2018.",

year = "2020",

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doi = "10.1093/imamci/dny035",

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N2 - We consider the equation $\textrm{d}u(t)/\textrm{d}t=A(t)u(t)$ with an unbounded operator $A(t)$ in a Hilbert space having a bounded strong derivative. We derive the exponential and $L^2$ stability conditions. An illustrative example is presented.

AB - We consider the equation $\textrm{d}u(t)/\textrm{d}t=A(t)u(t)$ with an unbounded operator $A(t)$ in a Hilbert space having a bounded strong derivative. We derive the exponential and $L^2$ stability conditions. An illustrative example is presented.

KW - differential equation in a Hilbert space

KW - linear non-autonomous equation

KW - stability

UR - https://www.scopus.com/pages/publications/85082064545

U2 - 10.1093/imamci/dny035

DO - 10.1093/imamci/dny035

M3 - Article

AN - SCOPUS:85082064545

SN - 0265-0754

VL - 37

SP - 19

EP - 26

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

IS - 1

ER -

Stability of linear equations with differentiable operators in a hilbert space

Abstract

Keywords

ASJC Scopus subject areas

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