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<HTML>
<HEAD><TITLE>AB05PD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="AB05PD">AB05PD</A></H2>
<H3>
Parallel inter-connection of two systems in state-space form
</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 compute the state-space model G = (A,B,C,D) corresponding to
the sum G = G1 + alpha*G2, where G1 = (A1,B1,C1,D1) and
G2 = (A2,B2,C2,D2). G, G1, and G2 are the transfer-function
matrices of the corresponding state-space models.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE AB05PD( OVER, N1, M, P, N2, ALPHA, A1, LDA1, B1, LDB1,
$ C1, LDC1, D1, LDD1, A2, LDA2, B2, LDB2, C2,
$ LDC2, D2, LDD2, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, INFO)
C .. Scalar Arguments ..
CHARACTER OVER
INTEGER INFO, LDA, LDA1, LDA2, LDB, LDB1, LDB2, LDC,
$ LDC1, LDC2, LDD, LDD1, LDD2, M, N, N1, N2, P
DOUBLE PRECISION ALPHA
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), A1(LDA1,*), A2(LDA2,*), B(LDB,*),
$ B1(LDB1,*), B2(LDB2,*), C(LDC,*), C1(LDC1,*),
$ C2(LDC2,*), D(LDD,*), D1(LDD1,*), D2(LDD2,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
OVER CHARACTER*1
Indicates whether the user wishes to overlap pairs of
arrays, as follows:
= 'N': Do not overlap;
= 'O': Overlap pairs of arrays: A1 and A, B1 and B,
C1 and C, and D1 and D, i.e. the same name is
effectively used for each pair (for all pairs)
in the routine call. In this case, setting
LDA1 = LDA, LDB1 = LDB, LDC1 = LDC, and LDD1 = LDD
will give maximum efficiency.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N1 (input) INTEGER
The number of state variables in the first system, i.e.
the order of the matrix A1, the number of rows of B1 and
the number of columns of C1. N1 >= 0.
M (input) INTEGER
The number of input variables of the two systems, i.e. the
number of columns of matrices B1, D1, B2 and D2. M >= 0.
P (input) INTEGER
The number of output variables of the two systems, i.e.
the number of rows of matrices C1, D1, C2 and D2. P >= 0.
N2 (input) INTEGER
The number of state variables in the second system, i.e.
the order of the matrix A2, the number of rows of B2 and
the number of columns of C2. N2 >= 0.
ALPHA (input) DOUBLE PRECISION
The coefficient multiplying G2.
A1 (input) DOUBLE PRECISION array, dimension (LDA1,N1)
The leading N1-by-N1 part of this array must contain the
state transition matrix A1 for the first system.
LDA1 INTEGER
The leading dimension of array A1. LDA1 >= MAX(1,N1).
B1 (input) DOUBLE PRECISION array, dimension (LDB1,M)
The leading N1-by-M part of this array must contain the
input/state matrix B1 for the first system.
LDB1 INTEGER
The leading dimension of array B1. LDB1 >= MAX(1,N1).
C1 (input) DOUBLE PRECISION array, dimension (LDC1,N1)
The leading P-by-N1 part of this array must contain the
state/output matrix C1 for the first system.
LDC1 INTEGER
The leading dimension of array C1.
LDC1 >= MAX(1,P) if N1 > 0.
LDC1 >= 1 if N1 = 0.
D1 (input) DOUBLE PRECISION array, dimension (LDD1,M)
The leading P-by-M part of this array must contain the
input/output matrix D1 for the first system.
LDD1 INTEGER
The leading dimension of array D1. LDD1 >= MAX(1,P).
A2 (input) DOUBLE PRECISION array, dimension (LDA2,N2)
The leading N2-by-N2 part of this array must contain the
state transition matrix A2 for the second system.
LDA2 INTEGER
The leading dimension of array A2. LDA2 >= MAX(1,N2).
B2 (input) DOUBLE PRECISION array, dimension (LDB2,M)
The leading N2-by-M part of this array must contain the
input/state matrix B2 for the second system.
LDB2 INTEGER
The leading dimension of array B2. LDB2 >= MAX(1,N2).
C2 (input) DOUBLE PRECISION array, dimension (LDC2,N2)
The leading P-by-N2 part of this array must contain the
state/output matrix C2 for the second system.
LDC2 INTEGER
The leading dimension of array C2.
LDC2 >= MAX(1,P) if N2 > 0.
LDC2 >= 1 if N2 = 0.
D2 (input) DOUBLE PRECISION array, dimension (LDD2,M)
The leading P-by-M part of this array must contain the
input/output matrix D2 for the second system.
LDD2 INTEGER
The leading dimension of array D2. LDD2 >= MAX(1,P).
N (output) INTEGER
The number of state variables (N1 + N2) in the resulting
system, i.e. the order of the matrix A, the number of rows
of B and the number of columns of C.
A (output) DOUBLE PRECISION array, dimension (LDA,N1+N2)
The leading N-by-N part of this array contains the state
transition matrix A for the resulting system.
The array A can overlap A1 if OVER = 'O'.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,N1+N2).
B (output) DOUBLE PRECISION array, dimension (LDB,M)
The leading N-by-M part of this array contains the
input/state matrix B for the resulting system.
The array B can overlap B1 if OVER = 'O'.
LDB INTEGER
The leading dimension of array B. LDB >= MAX(1,N1+N2).
C (output) DOUBLE PRECISION array, dimension (LDC,N1+N2)
The leading P-by-N part of this array contains the
state/output matrix C for the resulting system.
The array C can overlap C1 if OVER = 'O'.
LDC INTEGER
The leading dimension of array C.
LDC >= MAX(1,P) if N1+N2 > 0.
LDC >= 1 if N1+N2 = 0.
D (output) DOUBLE PRECISION array, dimension (LDD,M)
The leading P-by-M part of this array contains the
input/output matrix D for the resulting system.
The array D can overlap D1 if OVER = 'O'.
LDD INTEGER
The leading dimension of array D. LDD >= MAX(1,P).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The matrices of the resulting systems are determined as:
( A1 0 ) ( B1 )
A = ( ) , B = ( ) ,
( 0 A2 ) ( B2 )
C = ( C1 alpha*C2 ) , D = D1 + alpha*D2 .
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
None
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
None
</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>
* AB05PD EXAMPLE PROGRAM TEXT
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER N1MAX, N2MAX, NMAX, MMAX, PMAX
PARAMETER ( N1MAX = 20, N2MAX = 20, NMAX = N1MAX+N2MAX,
$ MMAX = 20, PMAX = 20 )
INTEGER LDA, LDA1, LDA2, LDB, LDB1, LDB2, LDC, LDC1,
$ LDC2, LDD, LDD1, LDD2
PARAMETER ( LDA = NMAX, LDA1 = N1MAX, LDA2 = N2MAX,
$ LDB = NMAX, LDB1 = N1MAX, LDB2 = N2MAX,
$ LDC = PMAX, LDC1 = PMAX, LDC2 = PMAX,
$ LDD = PMAX, LDD1 = PMAX, LDD2 = PMAX )
* .. Local Scalars ..
CHARACTER*1 OVER
INTEGER I, INFO, J, M, N, N1, N2, P
DOUBLE PRECISION ALPHA
* .. Local Arrays ..
DOUBLE PRECISION A(LDA,NMAX), A1(LDA1,N1MAX), A2(LDA2,N2MAX),
$ B(LDB,MMAX), B1(LDB1,MMAX), B2(LDB2,MMAX),
$ C(LDC,NMAX), C1(LDC1,N1MAX), C2(LDC2,N2MAX),
$ D(LDD,MMAX), D1(LDD1,MMAX), D2(LDD2,MMAX)
* .. External Subroutines ..
EXTERNAL AB05PD
* .. Executable Statements ..
*
OVER = 'N'
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) N1, M, P, N2, ALPHA
IF ( N1.LE.0 .OR. N1.GT.N1MAX ) THEN
WRITE ( NOUT, FMT = 99992 ) N1
ELSE
READ ( NIN, FMT = * ) ( ( A1(I,J), J = 1,N1 ), I = 1,N1 )
IF ( M.LE.0 .OR. M.GT.MMAX ) THEN
WRITE ( NOUT, FMT = 99991 ) M
ELSE
READ ( NIN, FMT = * ) ( ( B1(I,J), I = 1,N1 ), J = 1,M )
IF ( P.LE.0 .OR. P.GT.PMAX ) THEN
WRITE ( NOUT, FMT = 99990 ) P
ELSE
READ ( NIN, FMT = * ) ( ( C1(I,J), J = 1,N1 ), I = 1,P )
READ ( NIN, FMT = * ) ( ( D1(I,J), J = 1,M ), I = 1,P )
IF ( N2.LE.0 .OR. N2.GT.N2MAX ) THEN
WRITE ( NOUT, FMT = 99989 ) N2
ELSE
READ ( NIN, FMT = * )
$ ( ( A2(I,J), J = 1,N2 ), I = 1,N2 )
READ ( NIN, FMT = * )
$ ( ( B2(I,J), I = 1,N2 ), J = 1,M )
READ ( NIN, FMT = * )
$ ( ( C2(I,J), J = 1,N2 ), I = 1,P )
READ ( NIN, FMT = * )
$ ( ( D2(I,J), J = 1,M ), I = 1,P )
* Find the state-space model (A,B,C,D).
CALL AB05PD( OVER, N1, M, P, N2, ALPHA, A1, LDA1, B1,
$ LDB1, C1, LDC1, D1, LDD1, A2, LDA2, B2,
$ LDB2, C2, LDC2, D2, LDD2, N, A, LDA, B,
$ LDB, C, LDC, D, LDD, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
DO 20 I = 1, N
WRITE ( NOUT, FMT = 99996 )
$ ( A(I,J), J = 1,N )
20 CONTINUE
WRITE ( NOUT, FMT = 99995 )
DO 40 I = 1, N
WRITE ( NOUT, FMT = 99996 )
$ ( B(I,J), J = 1,M )
40 CONTINUE
WRITE ( NOUT, FMT = 99994 )
DO 60 I = 1, P
WRITE ( NOUT, FMT = 99996 )
$ ( C(I,J), J = 1,N )
60 CONTINUE
WRITE ( NOUT, FMT = 99993 )
DO 80 I = 1, P
WRITE ( NOUT, FMT = 99996 )
$ ( D(I,J), J = 1,M )
80 CONTINUE
END IF
END IF
END IF
END IF
END IF
STOP
*
99999 FORMAT (' AB05PD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from AB05PD = ',I2)
99997 FORMAT (' The state transition matrix of the connected system is')
99996 FORMAT (20(1X,F8.4))
99995 FORMAT (/' The input/state matrix of the connected system is ')
99994 FORMAT (/' The state/output matrix of the connected system is ')
99993 FORMAT (/' The input/output matrix of the connected system is ')
99992 FORMAT (/' N1 is out of range.',/' N1 = ',I5)
99991 FORMAT (/' M is out of range.',/' M = ',I5)
99990 FORMAT (/' P is out of range.',/' P = ',I5)
99989 FORMAT (/' N2 is out of range.',/' N2 = ',I5)
END
</PRE>
<B>Program Data</B>
<PRE>
AB05PD EXAMPLE PROGRAM DATA
3 2 2 3 1.0D0
1.0 0.0 -1.0
0.0 -1.0 1.0
1.0 1.0 2.0
1.0 1.0 0.0
2.0 0.0 1.0
3.0 -2.0 1.0
0.0 1.0 0.0
1.0 0.0
0.0 1.0
-3.0 0.0 0.0
1.0 0.0 1.0
0.0 -1.0 2.0
0.0 -1.0 0.0
1.0 0.0 2.0
1.0 1.0 0.0
1.0 1.0 -1.0
1.0 1.0
0.0 1.0
</PRE>
<B>Program Results</B>
<PRE>
AB05PD EXAMPLE PROGRAM RESULTS
The state transition matrix of the connected system is
1.0000 0.0000 -1.0000 0.0000 0.0000 0.0000
0.0000 -1.0000 1.0000 0.0000 0.0000 0.0000
1.0000 1.0000 2.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 -3.0000 0.0000 0.0000
0.0000 0.0000 0.0000 1.0000 0.0000 1.0000
0.0000 0.0000 0.0000 0.0000 -1.0000 2.0000
The input/state matrix of the connected system is
1.0000 2.0000
1.0000 0.0000
0.0000 1.0000
0.0000 1.0000
-1.0000 0.0000
0.0000 2.0000
The state/output matrix of the connected system is
3.0000 -2.0000 1.0000 1.0000 1.0000 0.0000
0.0000 1.0000 0.0000 1.0000 1.0000 -1.0000
The input/output matrix of the connected system is
2.0000 1.0000
0.0000 2.0000
</PRE>
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