EEL5173 Fall 2009 Lecture _18

EEL5173 Fall 2009 Lecture _18 - I. Multivariable Systems 2....

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Unformatted text preview: I. Multivariable Systems 2. Matrix Fraction Description (MFD) , , , , ), ( ) ( ), ( ) ( ) ( 1 1 L L R R L L R R P Q Q P where MFD Left a s P s Q MFD Right a s Q s P s G = = (RMFD) (LMFD) are matrices of polynomials. Common factor between P R and Q R ? Common factor between P L and Q L ? a matrix of rational functions p x q p x q q x q p x q p x p 3. Common Divisor For si-so systems, ) ( ) ( ) ( s d s n s G = When , ) ( ), ( ~ ), ( ~ ) ( ) ( ~ ) ( ) ( ) ( ~ ) ( s polynomial being s w s d s n with s w s d s d s w s n s n = = the polynomial w (s) is known as a common factor. Furthermore, ) ( ~ ) ( ~ ) ( ) ( ~ ) ( ) ( ~ ) ( ) ( ) ( ) ( ) ( ) ( ~ ) ( ) ( ) ( ~ s d s n s w s d s w s n s d s n s G s w s d s d s w s n s n = = = = = w (s) is also known as a common divisor. i. Common Right Divisor (crd) Given RMFD an s Q s P s G R R ), ( ) ( ) ( 1 = a matrix of polynomials V R , q x q , is known as a common right divisor if remain as matrices of polynomials. ) ( ) ( ) ( ) ( 1 1 s V s Q and s V s P R R R R p x q p x q q x q Note that [ ] [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 1 1 1 1 1 s Q s P s Q s V s V s P s V s Q s V s P R R R R R R R R R R = = Ex. [ ] 1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ) 2 ( ) 1 ( ) 2 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 2 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 2 ( ) 1 ( 1 ) 1 ( ) 1 ( ) 1 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 1 ( ) ( +...
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EEL5173 Fall 2009 Lecture _18 - I. Multivariable Systems 2....

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