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<HTML>
<HEAD><TITLE>SB08GD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="SB08GD">SB08GD</A></H2>
<H3>
State-space representation of a left coprime factorization
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To construct the state-space representation for the system
G = (A,B,C,D) from the factors Q = (AQR,BQ,CQR,DQ) and
R = (AQR,BR,CQR,DR) of its left coprime factorization
-1
G = R * Q,
where G, Q and R are the corresponding transfer-function matrices.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE SB08GD( N, M, P, A, LDA, B, LDB, C, LDC, D, LDD, BR,
$ LDBR, DR, LDDR, IWORK, DWORK, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDBR, LDC, LDD, LDDR, M, N, P
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), B(LDB,*), BR(LDBR,*), C(LDC,*),
$ D(LDD,*), DR(LDDR,*), DWORK(*)
INTEGER IWORK(*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix A. Also the number of rows of the
matrices B and BR and the number of columns of the matrix
C. N represents the order of the systems Q and R. N >= 0.
M (input) INTEGER
The dimension of input vector, i.e. the number of columns
of the matrices B and D. M >= 0.
P (input) INTEGER
The dimension of output vector, i.e. the number of rows of
the matrices C, D and DR and the number of columns of the
matrices BR and DR. P >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the state dynamics matrix AQR of the systems
Q and R.
On exit, the leading N-by-N part of this array contains
the state dynamics matrix of the system G.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,N).
B (input/output) DOUBLE PRECISION array, dimension (LDB,M)
On entry, the leading N-by-M part of this array must
contain the input/state matrix BQ of the system Q.
On exit, the leading N-by-M part of this array contains
the input/state matrix of the system G.
LDB INTEGER
The leading dimension of array B. LDB >= MAX(1,N).
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the leading P-by-N part of this array must
contain the state/output matrix CQR of the systems
Q and R.
On exit, the leading P-by-N part of this array contains
the state/output matrix of the system G.
LDC INTEGER
The leading dimension of array C. LDC >= MAX(1,P).
D (input/output) DOUBLE PRECISION array, dimension (LDD,M)
On entry, the leading P-by-M part of this array must
contain the input/output matrix DQ of the system Q.
On exit, the leading P-by-M part of this array contains
the input/output matrix of the system G.
LDD INTEGER
The leading dimension of array D. LDD >= MAX(1,P).
BR (input) DOUBLE PRECISION array, dimension (LDBR,P)
The leading N-by-P part of this array must contain the
input/state matrix BR of the system R.
LDBR INTEGER
The leading dimension of array BR. LDBR >= MAX(1,N).
DR (input/output) DOUBLE PRECISION array, dimension (LDDR,P)
On entry, the leading P-by-P part of this array must
contain the input/output matrix DR of the system R.
On exit, the leading P-by-P part of this array contains
the LU factorization of the matrix DR, as computed by
LAPACK Library routine DGETRF.
LDDR INTEGER
The leading dimension of array DR. LDDR >= MAX(1,P).
</PRE>
<B>Workspace</B>
<PRE>
IWORK INTEGER array, dimension (P)
DWORK DOUBLE PRECISION array, dimension (MAX(1,4*P))
On exit, DWORK(1) contains an estimate of the reciprocal
condition number of the matrix DR.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value;
= 1: the matrix DR is singular;
= 2: the matrix DR is numerically singular (warning);
the calculations continued.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The subroutine computes the matrices of the state-space
representation G = (A,B,C,D) by using the formulas:
-1 -1
A = AQR - BR * DR * CQR, C = DR * CQR,
-1 -1
B = BQ - BR * DR * DQ, D = DR * DQ.
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Varga A.
Coprime factors model reduction method based on
square-root balancing-free techniques.
System Analysis, Modelling and Simulation,
vol. 11, pp. 303-311, 1993.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
<HR>
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