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0 0.5 1 1.5−0.2

0

0.2

0.4

0.6

0.8

1

1.2

t[s]

θ2

estimation error

076" $" Estimation error for b&0

0 0.5 1 1.5−0.2

0

0.2

0.4

0.6

0.8

1

1.2

t[s]

θ2

θ2

estimated

076" %" Real and estimated velocity0

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x 10−3

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0

0.2

0.4

0.6

0.8

1

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estimation error

x 2es

timat

ion

erro

r

076" &" Graph of }b% vs }b&0

0 5 10 15 20 25 300

1

2

3

4

5

6

7

t[s]

[Kg

m2 /s

2 ]

Estimación del Parámetro

076" '" Parameter estimation !1?.

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0 5 10 15 20 25 30−4

−3

−2

−1

0

1

2

3

4

5

6

t[s]

1/t ∫ ε φ

076" (" The value of %D

33+0,5+0,2T00

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076" )" Estimation of Q$ via the traditional SMC/based parameter observer



076" *" Estimation of Q% via the traditional SMC/based parameter observer

076" +" Estimation of Q$ via the SOSM/based parameter observer

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076" $&" The time/varying parameter QD +the step/function, and its estimate Q!%"D 6

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30 A0F0 Filippov. :W!S_S[aWOY ;^bOaW\[` dWaV :W`Q\[aW[b\b` HWUVa*VO[R IWRS`. Dor/drecht. The Netherlands<Kluwer Academic Publishers= 3;::0

40 A0 Levant. Robust exact di!erentiation via sliding mode technique. 7ba\ZOaWQO.56+5,. 3;;:. pp0 59;/5:60

50 T0 Soderstrom. P0 Stoica. If`aSZ ?RS[aW"QOaW\[. Prentice Hall International=3;:;0

60 V0 Utkin. IYWRW[U C\RS` 9\[a_\Y O[R JVSW_ 7]]YWQOaW\[` a\ LO_WOPYS Ia_bQab_SIf`aSZ`. Mir. Moscow. 3;9:0



076" $'" The time/varying parameter QD+the step/function, and its estimate Q!&"D 6

70 V0 Utkin. J0 Guldner. J0 Shi. IYWRW[U C\RS 9\[a_\Y W[ ;YSQa_\ZSQVO[WQOY IfàSZ`.London. UK<Taylor ) Francis= 3;;;0

80 C0 Edwards and S0 Spurgeon. IYWRW[U C\RS 9\[a_\Y. Taylor ) Francis. Bristol.PA. 3;;:0

90 A0 Koshkouei and A0 Zinober. (Sliding mode observers for a class of nonlinearsystems.( F_\QSSRW[U` \T 7ZS_WQO[ 9\[a_\Y 9\[TS_S[QS. 4224. pp0 4328 / 43330

:0 F0 Floret/Pontet. F0 Lamnabhi/Lagarrigue. \Parameter Identi"cation Method/ology Using Sliding Mode Observers(. ?[a+ @\b_[OY \T 9\[a_\Y. vol0 96. No0 3:.4223. pp0 3965/39750

;0 A0 Levant. \Robust exact di!erentiation via sliding mode technique.( 7ba\ZOa*WQO) 56+5,. 3;;:. pp0 59;/5:60

320 L0 Ljung. *Asymptotic Behavior of the Extended Kalman Filter as a Parame/ter Estimator for Linear Systems*. ?;;; J_O[`+ 7ba+ 9\[a_\Y. -/!%'. 59/72.+3;9;,0

330 L0 Ljung. and S0 Gunnarsson. *Adaptation and Tracking in system Identi"cation/ A Survey*. 7ba\ZOaWQO. %). 9/43. +3;;2,0

340 P0 Eykho!. and P0 C0 Parks. *Identi"cation and System Parameter Estimation=Where do We Stand Now?* +Editorial,. 7ba\ZOaWQO. %). 5/7. +3;;2,0

350 G0 Lei and H0 F0 Chen. ?RS[aW"QOaW\[ O[R Ia\QVOàWQ 7RO]aWcS 9\[a_\Y0 Boston<Birkhauser.3;;30

360 W0 L0 Brogan. C\RS_[ 9\[a_\Y JVS\_f. 5rd edition. Prentice Hall. New Jersey.3;;30

370 Y0 B0 Shtessel. and A0 S0 Poznyak. \Parameter Identi"cation of AÆne TimeVarying Systems Using Traditional and High Order Sliding Modes.( F_\QSSRW[U`\T 7ZS_WQO[ 9\[a_\Y 9\[TS_S[QS. vol0 6. 4227. pp0 4655/465:0

380 Y0 B0 Shtessel. and A0 S0 Poznyak. \Parameter identi"cation of linear timevarying systems via traditional and high order sliding modes.( F_\QSSRW[U` \T4aV ?[aS_[OaW\[OY M\_X`V\] \[ LO_WOPYS Ia_bQab_S IfàSZ`. Spain. Villanova.September 8/:.

390 M0F0 Chun and T0S0 Han. \Real time parameters identi"cation of ship dynamicusing the extended Kalman "lter and the second order "lter.( ?;;; 9\[TS_S[QS+\[ 9\[a_\Y 7]]YWQOaW\[` * F_\QSSRW[U`. V04. 4225. pp0 3467/34720

3:0 A0 S0 Poznyak. and J0 Medel. \Matrix Forgetting Factor.( ?[a+ @\b_[OY \T If`*aSZ` IQWS[QS. vol0 52. No< 4. 3;;;. pp0 387/3960

3;0 A0 S0 Poznyak. and J0 Medel. \Matrix Forgetting with Adaptation.( ?[a+ @\b_[OY\T IfàSZ` IQWS[QS. vol0 52. No0:. 3;;;. pp0 :87/:9:0

420 A0 S0 Poznyak. *Estimating de Parameters of Autoregression Process by theMethod of Least Squares*. ?[a+ @+ I9?0. 3;:2. $$. 799/7::0

430 S0 Sheikholeslam. *Observer Based Parameter Identi"er for Nonlinear Systemswith Parameter Dependencies*. ?;;; J_O[`+ 7ba+ 9\[a_\Y. -/!'#. 5:4/:9.3;;70

440 Song. Y0 D0. Adaptive Parameter Estimators for a Class of Nonlinear Systems.?[a+ @+ 7RO]a+ 9\[a_\Y IWU[OY F_\QS``+. $$. 863/86:. 3;;90

450 A0 S0 Poznyak. Stochastic output noise e!ects in sliding mode state estimation.?[a+ @\b_[OY 9\[a_\Y. vol0 98. ;132. 4225. pp0 ;:8/32220

460 A0 Bensoussan. Ia\QVOàWQ 9\[a_\Y \T FO_aWOYYf EP`S_cOPYS IfàSZ`. CambridgeUniversity Press. Cambridge. UK. 3;;40

470 M0 Basin. MAA0 Garcia. Optimal "ltering and control for third degree poly/nomial system. :f[OZWQ` \T 9\[aW[b\b`) :W`Q_SaS) O[R ?Z]bY`WcS IfàSZ`. vol032B. 4225. pp0 885/8:20

480 M0 Basin. Optimal "ltering for polynomial system states. 7IC; J_O[ÒQaW\[`+@+ \T :f[OZWQ IfàSZ`) CSO`b_SZS[a) O[R 9\[a_\Y. vol0 347. 4225. pp0 345/3470

490 M0 V0 Basin and M0 Skliar. \Optimal "ltering for partially measured polynomialsystem states.( F_\QSSRW[U` \T 7ZS_WQO[ 9\[a_\Y 9\[TS_S[QS. vol0 8. 4227. pp06244/62490

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