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עמוד:*27
stable Filippov DI n � ζ 0 � n λ ˜ − = 0 ζ ˙ n + 1 + ζ 1 , . . . n − 1 = − ˜ λ 1 � ζ 0 � 1 ζ ˙ n + 1 + ζ n , n ∈ − ˜ λ 0 sign ( ζ 0 ) + [ − 1 , 1 ] , ζ ˙ ) 11 ( where KF [ sign ( · ) ] ( 0 ) = [ − 1 , 1 ] is substituted for sign 0 when ζ 0 = 0 . The error dynamics ( 11 ) are homogeneous with deg ζ i = n + 1 − i , deg t = 1 and coincide with the error dynamics of the standard differentiator, corresponding to n d = n , n f = 0 . Hence, the standard features are directly extended to the filtering differentiators . In particular, parameters ˜ λ i , i = 0 , . . . , n , are the same for all n d , n f keeping n d + n f = n . It was shown that the steady state accuracies w 1 | ≤ γ w 1 Lρ n f + n d + 1 | , � � z i − f ( i ) � t ) � ( 0 � i Lρ n d + 1 − i γ ≤ � i = 0 , . . . , n d ( 12 ) , w j | ≤ γ w j Lρ n d + n f + 2 − j | j = 2 , . . . , n f , ( 13 ) , are in FTestablished for L ) 1 / 0 ε ( = ρ nd + 1 ) , ( 14 ) ( and some γ w 1 , γ w j , γ i > 0 only depending on the choice of ˜ λ 0 , . . . , ˜ λ n d + n f . It means that describe an alternative asymptotically optimal n d th - order differentiator . ) 10 ( , ) 9 ( This differentiator has significant filtering properties . The accuracy estimation ( 13 ) is singled out, since it does not hold for the corresponding ρ in the presence of large noises considered there . * 27
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אדמוני, אריאל
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