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HAL Id: hal-00845633

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Submitted on 17 Jul 2013

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Guaranteed robust nonlinear minimax estimation

Luc Jaulin, Eric Walter

To cite this version:

Luc Jaulin, Eric Walter. Guaranteed robust nonlinear minimax estimation. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2002, 47 (11), pp.1857-1864.

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Guaranteed Robust Nonlinear

Minimax Estimation

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(16)

!"#$% &' ()% *+,-. */0 !1 2)% 3!42%$1%-2!/4 /5 ! */0%16 5.4 Application to robust minimax estimation

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(17)

!" #$% &%'(&)*+% *,-.%,%!# #*/! 0123 ' ! 4% " -#%" #/ #$*) '/!#%5# #/ '/,-(#% !6

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6 Test case

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HS

(18)

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>E

(19)

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!"!$

7 Conclusions

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%1(% (,& )2-&+&2-&2%4$ .2)0",'4$ -)#%,)6.%&- "3&, %1& )2%&,3(4 !%# %!5 9)%1 % .2:2"925 ')2)'(/

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&#%)'(%&# %1.# -&<2&- )2 ( .2)"2 "0 6"/&# )2 +(,('&%&, #+(*&5 &3&2 )2 %1& *(#& 91&,& %1& '"-&4 )# 2"24)2&(, )2 )%# +(,('&%&,# (2- %1& &#%)'(%&# (,& 2"% .2)=.&5 (# )44.#%,(%&- 6$ (2 &/('+4&

>" %1& 6&#% "0 "., :2"94&-8&5 %1&,& )# 2" "%1&, '&%1"- (3()4(64& )2 %1& 4)%&,(%.,& %" -&(4 9)%1

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IJ

(20)

References

!" #$ %&''())*+ ,$ -./(0+ ,$1$ 2)34(5+ &04 1$6$ 78&45&9$ !"#$%&"'()*'&" )"+ ,'"-)%'*!. /"

/01-2%) 3&% 4'5#%-*- 67-"* !5*-85$ 1./0 :*)(; < =.03+ >(? @.5A+ !BBC$

C" D$:$ %&* &04 E$ -/.$ F*0*G*H&9*.0 ?*9/ I(? J*.)&9(4 '.0395&*093 &04 *93 &KK)*'&9*.0 *0 3(9LG(GM(53/*K *4(09*N'&9*.0$ O0 9%&#. :;/< =&%+ <&"1%-55+ J.)8G( E+ K&P(3 QRQSQRT+

%(*U*0P+ -/*0&+ !BBB$

Q" #$ %(0/&G.8 &04 V$ ,5&0J*))*(53$ W89.G&9*' P(0(5&9*.0 .I 08G(5*'&) 5(4804&0'*(3 I.5 0.0)*0(&5 '.0395&*09 3.)J*0P$ >-0')20- <&8?@*'"1+ K&P(3 QQXSQRR+ !BBY$

R" #$ %(0/&G.8 &04 :$ 2)4(5$ WKK);*0P *09(5J&) &5*9/G(9*' 9. 5(&)+ *09(P(5 &04 %..)(&0 '.0395&*093$ A&@%")0 &3 ,&1'# 9%&1%)88'"1+ K&P(3 !SCR+ !BBY$

X" #$ V$ -/(50.83A.$ *)*- 65*'8)*'&" 3&% 4!")8'# !5*-85$ -Z- 65(33+ !BBR$

[" 1$ -$ -)(&5;$ V.P*'&) &5*9/G(9*'$ ;@*@%- <&8?@*'"1 !5*-85+ C\C]^!CXS!RB+ !BTY$

Y" D$ _&J*3$ -.0395&*09 K5.K&P&9*.0 ?*9/ *09(5J&) )&M()3$ /%*'B#')0 :"*-00'1-"#-+ QC^CT!SQQ!+

!BTY$

T" D$ Z$ E&03(0$ C0&2)0 D?*'8'()*'&" @5'"1 :"*-%7)0 /")0!5'5$ F&5'() _(AA(5+ >(? @.5A+

!BBC$

B" 6$ `&0 E(09(05;'A+ @$ _(J*))(+ &04 V$ F*'/()$ E@8-%'#). / F&+-0'"1 ,)"1@)1- 3&% C0&2)0 D?*'8'()*'&"$ FOa 65(33+ %.39.0+ !BBY$

!b" D$ E;J.0(0$ -.0395&*09 5(&3.0*0P M&3(4 .0 *09(5J&) &5*9/G(9*'c 9/( 9.)(5&0'( K5.K&P&9*.0

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