Lecture Notes in Control and Information Sciences Editors: M. Thoma · M. Morari
278
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Lecture Notes in Control and Information Sciences Editors: M. Thoma · M. Morari
278
Springer Berlin Heidelberg NewYork Barcelona Hong Kong London Milan Paris Tokyo
Chunling Du and Lihua Xie
H∞ Control and Filtering of Two-dimensional Systems With 32 Figures
13
Series Advisory Board
A. Bensoussan · P. Fleming · M.J. Grimble · P. Kokotovic · A.B. Kurzhanski · H. Kwakernaak · J.N. Tsitsiklis
Author Dr. Chunling Du Data Storage Institute Engineering Nr. 1 Singapore 117608 Singapore
Prof. Lihua Xie School of Electrical and Electronic Technological University Nanyang Avenue Singapore 639798 Singapore
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek – CIP-Einheitsaufnahme Du, Chunling: H∞ control and filtering of two-dimensional systems / Chunling Du and Lihua Xie. Berlin ; Heidelberg ; NewYork ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in control and information sciences ; 278) (Engineering online library) ISBN 3-540-43329-5
ISBN 3-540-43329-5
Springer-Verlag Berlin Heidelberg New York
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Digital data supplied by author. Data-conversion by PTP-Berlin, Stefan Sossna e.K. Cover-Design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN 10869692 62/3020Rw - 5 4 3 2 1 0
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hjþ¸¹ BP e-s8}j¸ ÿdÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ
ÿn
qY¸ ý7e BP þY¸ 1T*
ÿ;
ýs-$8Z8 R$tüZjs¹ %sjZ¸ BP þY¸ þ¹stRP¸¹ PZt{þ$Bt 8sþ¹$- BP þY¸
ÿx
qY¸ R$ütsj
hjþ¸¹$tü ¸¹¹B¹ RkRþ¸8ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ
?d w7, i D BP ¸Rþ$8sþ¸ ? |d w7, i D
ûn
û;
e-s8}j¸ ÿ1ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ
ûx
BP e-s8}j¸ ÿ1ÿ
ÿÿ ÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ ÿÿ
ûx
hjþ¸¹ BP e-s8}j¸ ÿ1ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ
ûE
ÿE
qY¸
ÿ
qY¸ ý7e BP þY¸ 1T*
ÿM
ýs-$8Z8 R$tüZjs¹ %sjZ¸R }jBþ BP þY¸ þ¹stRP¸¹ PZt{þ$Bt 8sþ¹$- BP
ÿû
ýs-$8Z8 R$tüZjs¹ %sjZ¸R }jBþ BP þY¸ þ¹stRP¸¹ PZt{þ$Bt 8sþ¹$- BP
þ
I
þY¸ hjþ¸¹$tü ¸¹¹B¹ RkRþ¸8ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ
þY¸ hjþ¸¹$tü ¸¹¹B¹ RkRþ¸8ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ
û
ûM
Mÿd
qY¸ $t}Zþ $8sü¸ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ddd
Mÿ1
qY¸ $8sü¸ A¸PB¹¸ I¸{Bt%BjZþ$Bt }¹B{¸RR$tü bY¸t þY¸ 8¸sRZ¹¸8¸tþ
Mÿn
qY¸ $8sü¸ sPþ¸¹ I¸{Bt%BjZþ$Bt }¹B{¸RR$tü bY¸t þY¸ 8¸sRZ¹¸8¸tþ
Mÿ;
qY¸ $8sü¸ sPþ¸¹ ¹BAZRþ I¸{Bt%BjZþ$Bt hjþ¸¹$tü bY¸t þY¸ 8¸sRZ¹¸T
7Wi $R dEÿEIúÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dd1
7Wi $R dEÿEIúÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dd1
8¸tþ 7Wi $R dEÿE Iúÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dd;
XII
List of Figures
ûÿd
V8}j$þZI¸ ¹¸R}BtR¸ PB¹ B¹$ü$tsj w1_, 18D hjþ¸¹ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ d1E
ûÿ1
V8}j$þZI¸ ¹¸R}BtR¸ BP I
ûÿn
V8}j$þZI¸ ¹¸R}BtR¸ BP þY¸ RkRþ¸8 t
ûÿ;
V8}j$þZI¸ ¹¸R}BtR¸ PB¹ B¹$ü$tsj w;_, M8D hjþ¸¹ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dnd
ûÿx
V8}j$þZI¸ ¹¸R}BtR¸ BP I
ûÿE
V8}j$þZI¸ ¹¸R}BtR¸ BP þY¸ RkRþ¸8 t
ûÿ
V8}j$þZI¸ ¹¸R}BtR¸ PB¹ B¹$ü$tsj wd_, ;8D hjþ¸¹ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dn;
ÿ
ÿ
ÿ
w1_, d8D ¹¸IZ{¸ITB¹I¸¹ hjþ¸¹ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ d1
ÿ
| tÿ
ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ d1
w;_, ;8D ¹¸IZ{¸ITB¹I¸¹ hjþ¸¹ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dnd
ÿ
| tÿ
ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dn1
wd_, 18D ¹¸IZ{¸ITB¹I¸¹ hjþ¸¹ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dn;
ûÿM
V8}j$þZI¸ ¹¸R}BtR¸ BP I
ûÿû
V8}j$þZI¸ ¹¸R}BtR¸ BP þY¸ RkRþ¸8 t
ÿ
| tÿ
ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ dnx
7k8ABjR stI V{Btk8R
1T*U
þbBTI$8¸tR$Btsjÿ
dT*U
Bt¸TI$8¸tR$Btsjÿ
NýyU
j$t¸s¹ 8sþ¹$- $t¸JZsj$þkÿ
ViyU
sjü¸A¹s${ i${{sþ$ $t¸JZsj$þkÿ
i*yU
i${{sþ$ I$&¸¹¸t{¸ $t¸JZsj$þkÿ
i*eU
i${{sþ$ I$&¸¹¸t{¸ ¸JZsþ$Btÿ
©U
R¸þ BP $tþ¸¹ü¸¹ tZ8A¸¹Rÿ
7, i U
$tþ¸ü¸¹T%sjZ¸I %¸¹þ${sj stI YB¹$9Btþsj {BB¹I$tsþ¸Rÿ
oz U
zTI$8¸tR$Btsj ¹¸sj eZ{j$I¸st R}s{¸ÿ
ozýE U
R¸þ BP z
z
{ U
z
\
I$sü \d , \1 ,
N N N , \z iU
þ E ¹¸sj 8sþ¹${¸Rÿ
þ z $I¸tþ$þk 8sþ¹$-ÿ
i
AjB{, I$süBtsj 8sþ¹$- b$þY \ w tBþ t¸{¸RRs¹$jk RJZs¹¸D Bt þY¸ I$süBtsjÿ
¼
x
¼
d 1U
U
b
þ¹stR}BR¸ BP 8sþ¹$- ¼ ÿ
s Rk88¸þ¹${ RJZs¹¸ ¹BBþ BP s 8sþ¹$- ¼ ) ¼ $ÿ¸ÿù
h
ý (U
h k (U
b
b
d 1¼ d 1 ¼
xý
(ù
) ¼ÿ
Rk88¸þ¹${ }BR$þ$%¸ R¸8$I¸ht$þ¸ 8sþ¹$- h
Rk88¸þ¹${ }BR$þ$%¸ I¸ht$þ¸ 8sþ¹$- h
; ozýz ÿ
; ozýz ÿ
XIV
Symbols and Acronyms
ý
h
ÿ<ý(
PB¹ Rk88¸þ¹${ h, <
; ozýz ÿ
h k
h
ÿ
PB¹ Rk88¸þ¹${ h, <
; ozýz ÿ
þ8s- w¼ D U
8s-$8Z8 R$tüZjs¹ %sjZ¸ BP 8sþ¹$- ¼ ÿ
h
· ý¹w¼ D B¹
[ w¼ DU
ow¼ DU ¼
üU
tZjj R}s{¸ BP j$t¸s¹ B}¸¹sþB¹ ¼ ÿ
¹stü¸ R}s{¸ BP j$t¸s¹ B}¸¹sþB¹ ¼ ÿ
8sþ¹$- Rsþ$RPk$tü stI ¼
, N ,U ,j ,1
\
[ w¼ ü D ) ow¼ D
k (ÿ
eZ{j$I¸st %¸{þB¹ tB¹8ÿ
U
üD, >(, üDiU
7)( i )(
\jw7, i Diù
,jw7, i D,1 3
R}s{¸ BP RJZs¹¸ RZ88sAj¸ R¸JZ¸t{¸R Bt
F7 w7 ) d, 1DU
ÿ þþ þþ
f1 TtB¹8 BP s 1T* I$R{¹¸þ¸Tþ$8¸ R$ütsj $ÿ¸ÿù
f1 >(,
ü ¼ üx
\>(, üD, >(, üDi
b$þY %sjZ¸R Bt
1T* FTþ¹stRPB¹8 %s¹$sAj¸Rÿ
oz ÿ
2$ 87#<+,09#'+7
2$2 &(;<(';1
!%¸¹ ÿY¸ }sRÿ R¸%¸¹sj I¸{sI¸Rþ s {BtR$I¸¹sAj¸ $tÿ¸¹¸Rÿ YsR A¸¸t I¸%Bÿ¸I ÿB }¹BAj¸8R $t%Bj%$tý R$ýtsjR stI RkRÿ¸8R ÿYsÿ I¸}¸tI Bt 8B¹¸ ÿYst Bt¸ %s¹$T sAj¸ü 1T* R$ýtsjR stI RkRÿ¸8R Ys%¸ A¸¸t RÿZI$¸I $t ¹¸jsÿ$Bt ÿB R¸%¸¹sj 8BI¸¹t ¸tý$t¸¸¹$tý h¸jIR RZ{Y sR }¹B{¸RR {Btÿ¹Bjþ 8Zjÿ$TI$8¸tR$Btsj w8T*D I$ý$ÿsj hjT ÿ¸¹$týþ $8sý¸ ¸tYst{¸8¸tÿþ $8sý¸ I¸AjZ¹¹$týþ R$ýtsj }¹B{¸RR$týþ ¸ÿ{ü V8Btý ÿY¸ 8sÁB¹ ¹¸RZjÿR I¸%¸jB}¸I RB Ps¹ {Bt{¸¹t$tý ÿY¸ 1T* R$ýtsjR stI RkRÿ¸8Rþ 1T * I$ý$ÿsj hjÿ¸¹R s¹¸ $t%¸Rÿ$ýsÿ¸I sR s I¸R{¹$}ÿ$Bt $t P¹¸JZ¸t{k IB8s$t B¹ sR s {Bt%BjZÿ$Bt BP ÿY¸ $t}Zÿ stI ÿY¸ Zt$ÿ $8}ZjR¸ ¹¸R}BtR¸ü yÿR ý¹¸sÿ }Bÿ¸tÿ$sj PB¹ }¹s{ÿ${sj s}}j${sÿ$BtR $t ÿY¸ 1T* $8sý¸ stI R$ýtsj }¹B{¸RR$tý YsR A¸¸t RYBbt >E;H>ExHü !t ÿY¸ BÿY¸¹ YstIþ s ÿ¸{Yt${sjjk %¸¹k $8}B¹ÿstÿ ¹stý¸ BP 1T* }¹BAT j¸8R ¸-$Rÿ bY${Y ¹¸JZ$¹¸ P¸¸IAs{, {Btÿ¹Bj >;;Hü 1T* {Btÿ¹Bj YsR }¹¸%$BZRjk A¸¸t s}}¹Bs{Y¸I P¹B8 s }¹¸IB8$tstÿjk RkRÿ¸8R ÿY¸B¹¸ÿ${sj }B$tÿ BP %$¸bü qY$R YsR ÿbB 8s$t A¹st{Y¸Rþ R¸¸t $t >E(H>1Hþ ÿs,$tý st $t}ZÿTBZÿ}Zÿ ÿ¹stRP¸¹ PZt{ÿ$Bt s}}¹Bs{Y stI s Rÿsÿ¸TR}s{¸ s}}¹Bs{Yþ ¹¸R}¸{ÿ$%¸jkü 1T* Rÿsÿ¸TR}s{¸ 8BI¸jRþ YBb¸%¸¹þ Ys%¸ sÿÿ¹s{ÿ¸I s jBÿ BP $tÿ¸¹¸Rÿ IZ¸ ÿB $ÿR sI%stÿsý¸ BP }¹BT %$I$tý s R$8}j¸ stI $tÿZ$ÿ$%¸ ¹¸R¸s¹{Y 8¸ÿYBI PB¹ 1T* R$ýtsjR stI RkRÿ¸8Rü VjÿYBZýY $ÿ s}}¸s¹R RB8¸ÿY$tý j$,¸ ÿY¸ Bt¸TI$8¸tR$Btsj wdT*D Rÿsÿ¸ R}s{¸ 8BI¸jþ ÿY¸¹¸ ¸-$Rÿ RB8¸ ¸RR¸tÿ$sj I$&¸¹¸t{¸R A¸ÿb¸¸t ÿY¸8ü qY¸¹¸PB¹¸þ 1T* Rÿsÿ¸TR}s{¸ ¹¸}¹¸R¸tÿsÿ$BtR Ys%¸ A¸¸t ¸-ÿ¸tR$%¸jk RÿZI$¸I ÿY¸B¹¸ÿ${sjjk stI }¹s{ÿ${sjjkü 1T* Rÿsÿ¸TR}s{¸ ÿY¸B¹k B¹$ý$tsÿ¸I P¹B8 iB¸RR¸¹ >nxH>EH bYB }¹BIZ{¸I ÿY¸ {¸j¸A¹sÿ¸I iBRR¸¹ 8BI¸j bY¸t Y¸ RÿZI$¸I ÿY¸ 8Zjÿ$TI$8¸tR$Btsj j$t¸s¹ $ÿT ¸¹sÿ$%¸ {$¹{Z$ÿR sÿ ÿY¸ A¸ý$tt$tý BP ÿY¸ R¸%¸tÿ$¸Rü 7$t{¸ ÿY¸tþ R¸%¸¹sj BÿY¸¹ R{YBjs¹R RZ{Y sR VÿÿsR$ >xHþ 3B¹tsR$t$ stI ûs¹{Y¸R$t$ >1MH stI ·Z¹¸, >xMH Ys%¸ I¹sbt ÿY¸ VÿÿsR$ 8BI¸jþ ÿY¸ 3û N77 w3B¹tsR$t$Tûs¹{Y¸R$t$ jB{sj Rÿsÿ¸T R}s{¸D 8BI¸j stI ÿY¸ p¸t¸¹sj 8BI¸jþ ¹¸R}¸{ÿ$%¸jk P¹B8 ÿY¸$¹ Bbt I$&¸¹¸tÿ ¹¸R¸s¹{Y h¸jIRü qY¸ ¹¸jsÿ$BtRY$}R A¸ÿb¸¸t ÿY¸R¸ 8BI¸jR s¹¸ I¸ÿs$j¸I $t >xdHü úsR¸I Bt ÿY¸R¸ Rÿsÿ¸TR}s{¸ I¸R{¹$}ÿ$BtRþ R¸%¸¹sj }¹B}¸¹ÿ$¸R BP 1T* RkRÿ¸8R RZ{Y sR {Btÿ¹BjjsA$j$ÿkþ BAR¸¹%sA$j$ÿkwR¸¸þ PB¹ ¸-s8}j¸þ >1;Hþ >xùH stI ÿY¸ ¹¸P¸¹T ¸t{¸R ÿY¸¹¸$tDþ RÿsA$j$ÿk >1H>nHþ ¹¸sj$9sÿ$Bt >1xHþ ¸ÿ{þ Ys%¸ A¸¸t $t%¸Rÿ$ýsÿ¸Iü ûB¹¸B%¸¹þ 1T* P¸¸IAs{, I¸R$ýt ÿ¸{Yt$JZ¸R RZ{Y sR ¸$ý¸t%sjZ¸ sRR$ýt8¸tÿ >x1Hþ RÿsA$j$9sÿ$Bt >;EH stI BAR¸¹%¸¹R >MH>ùEH Ys%¸ ¹¸{¸$%¸I {BtR$I¸¹sAj¸ sÿÿ¸tÿ$Btü Ch. Du, L. Xie:
Control and Filtering of Two-dimensional Systems, LNCIS 278, pp. 1−4, 2002.
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Ch. Du, L. Xie:
Control and Filtering of Two-dimensional Systems, LNCIS 278, pp. 5−25, 2002.
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Ch. Du, L. Xie:
Control and Filtering of Two-dimensional Systems, LNCIS 278, pp. 81−98, 2002.
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Control and Filtering of Two-dimensional Systems, LNCIS 278, pp. 137−138, 2002.
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