EEL5173 Fall 2009 Lecture _24

EEL5173 Fall 2009 Lecture _24 - ii. Observer-Form...

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Theorem. Let Q ( s ) be a p x p matrix of polynomials and be represented by its row vectors as shown: = p P P P Q M 2 1 {} . , , 2 , 1 , deg p i p P i i L = = Let Then, {} = p i i p Q 1 deg Q ( s ) is said to be row-reduced if {} = = p i i p Q 1 deg ii. Observer-Form Realization (1) Row-reduced Non-Singular Matrix of Polynomials given a co-prime LMFD, G ( s )= Q L - 1 P L .
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Ex. + + = 1 1 1 ) ( 2 3 s s s s s Q p 1 =3 {} { } . , 5 2 3 2 1 ) 1 ( 1 deg deg 2 1 2 2 3 reduced row not p s s s s s s Q i i = + = < = = + + = = p 2 =2
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Definition. Let Q ( s ) be a p x p matrix of polynomials and be represented by its row vectors as shown: = p P P P Q M 2 1 { } . , , 2 , 1 , deg p i p P i i L = = Let be the coefficient row vector of terms in P i , i = 1, 2, . .., p . i w r i p s = p def hr w w w Q r M r r 2 1 - the highest-row-degree coefficient matrix.
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Ex. + + = 1 1 1 ) ( 2 3 s s s s s Q p 1 =3 p 2 =2 = = 0 1 0 1 2 1 w w Q hr r r Theorem. Let Q ( s ) be a p x p matrix of polynomials. It is row-reduced if and only if the highest-row-degree coefficient matrix, Q hr , is non-singular.
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Theorem. Let
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This note was uploaded on 07/15/2011 for the course EEL 5173 taught by Professor Tung during the Fall '09 term at FSU.

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EEL5173 Fall 2009 Lecture _24 - ii. Observer-Form...

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