Smith method for projected Lyapunov and Stein equations

Bo Yu; Hung Yuan Fan; Eric King Wah Chu

Smith method for projected Lyapunov and Stein equations

Bo Yu^*, Hung Yuan Fan, Eric King Wah Chu

^*Corresponding author for this work

Department of Mathematics

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

3 Citations (Scopus)

Abstract

We consider the projected Lyapunov and Stein equations arising in model order reduction and optimal control of descriptor systems. The projected Lyapunov equation is transformed to an equivalent projected Stein equation then solved by a generalized Smith iterative method. For a projected general Stein equation with a singular matrix "E", a double Cayley transform is devised to remove the singularity, and then the generalized Smith method is applied. Numerical examples are provided to demonstrate the feasibility and efficiency of our approach.

Original language	English
Pages (from-to)	191-204
Number of pages	14
Journal	UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
Volume	80
Issue number	2
Publication status	Published - 2018

Keywords

Cayley transform
Descriptor system
Double Cayley transform
Projected Lyapunov equation
Projected Stein equation

ASJC Scopus subject areas

General Physics and Astronomy
Applied Mathematics

Cite this

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title = "Smith method for projected Lyapunov and Stein equations",

abstract = "We consider the projected Lyapunov and Stein equations arising in model order reduction and optimal control of descriptor systems. The projected Lyapunov equation is transformed to an equivalent projected Stein equation then solved by a generalized Smith iterative method. For a projected general Stein equation with a singular matrix {"}E{"}, a double Cayley transform is devised to remove the singularity, and then the generalized Smith method is applied. Numerical examples are provided to demonstrate the feasibility and efficiency of our approach.",

keywords = "Cayley transform, Descriptor system, Double Cayley transform, Projected Lyapunov equation, Projected Stein equation",

author = "Bo Yu and Fan, {Hung Yuan} and Chu, {Eric King Wah}",

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language = "English",

volume = "80",

pages = "191--204",

journal = "UPB Scientific Bulletin, Series A: Applied Mathematics and Physics",

issn = "1223-7027",

publisher = "Politechnica University of Bucharest",

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TY - JOUR

T1 - Smith method for projected Lyapunov and Stein equations

AU - Yu, Bo

AU - Fan, Hung Yuan

AU - Chu, Eric King Wah

PY - 2018

Y1 - 2018

N2 - We consider the projected Lyapunov and Stein equations arising in model order reduction and optimal control of descriptor systems. The projected Lyapunov equation is transformed to an equivalent projected Stein equation then solved by a generalized Smith iterative method. For a projected general Stein equation with a singular matrix "E", a double Cayley transform is devised to remove the singularity, and then the generalized Smith method is applied. Numerical examples are provided to demonstrate the feasibility and efficiency of our approach.

AB - We consider the projected Lyapunov and Stein equations arising in model order reduction and optimal control of descriptor systems. The projected Lyapunov equation is transformed to an equivalent projected Stein equation then solved by a generalized Smith iterative method. For a projected general Stein equation with a singular matrix "E", a double Cayley transform is devised to remove the singularity, and then the generalized Smith method is applied. Numerical examples are provided to demonstrate the feasibility and efficiency of our approach.

KW - Cayley transform

KW - Descriptor system

KW - Double Cayley transform

KW - Projected Lyapunov equation

KW - Projected Stein equation

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M3 - Article

AN - SCOPUS:85047897899

SN - 1223-7027

VL - 80

SP - 191

EP - 204

JO - UPB Scientific Bulletin, Series A: Applied Mathematics and Physics

JF - UPB Scientific Bulletin, Series A: Applied Mathematics and Physics

IS - 2

ER -

Smith method for projected Lyapunov and Stein equations

Abstract

Keywords

ASJC Scopus subject areas

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