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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
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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