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<HTML>
<HEAD><TITLE>AB05SD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="AB05SD">AB05SD</A></H2>
<H3>
Closed-loop system for an output feedback control law
</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 for a given state space system (A,B,C,D) the closed-
loop system (Ac,Bc,Cc,Dc) corresponding to the output feedback
control law
u = alpha*F*y + v.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE AB05SD( FBTYPE, JOBD, N, M, P, ALPHA, A, LDA, B, LDB,
$ C, LDC, D, LDD, F, LDF, RCOND, IWORK, DWORK,
$ LDWORK, INFO)
C .. Scalar Arguments ..
CHARACTER FBTYPE, JOBD
INTEGER INFO, LDA, LDB, LDC, LDD, LDF, LDWORK, M, N, P
DOUBLE PRECISION ALPHA, RCOND
C .. Array Arguments ..
INTEGER IWORK(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*),
$ DWORK(*), F(LDF,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
FBTYPE CHARACTER*1
Specifies the type of the feedback law as follows:
= 'I': Unitary output feedback (F = I);
= 'O': General output feedback.
JOBD CHARACTER*1
Specifies whether or not a non-zero matrix D appears in
the given state space model:
= 'D': D is present;
= 'Z': D is assumed a zero matrix.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The number of state variables, i.e. the order of the
matrix A, the number of rows of B and the number of
columns of C. N >= 0.
M (input) INTEGER
The number of input variables, i.e. the number of columns
of matrices B and D, and the number of rows of F. M >= 0.
P (input) INTEGER
The number of output variables, i.e. the number of rows of
matrices C and D, and the number of columns of F. P >= 0
and P = M if FBTYPE = 'I'.
ALPHA (input) DOUBLE PRECISION
The coefficient alpha in the output feedback law.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the system state transition matrix A.
On exit, the leading N-by-N part of this array contains
the state matrix Ac of the closed-loop system.
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 system input matrix B.
On exit, the leading N-by-M part of this array contains
the input matrix Bc of the closed-loop system.
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 system output matrix C.
On exit, the leading P-by-N part of this array contains
the output matrix Cc of the closed-loop system.
LDC INTEGER
The leading dimension of array C.
LDC >= MAX(1,P) if N > 0.
LDC >= 1 if N = 0.
D (input/output) DOUBLE PRECISION array, dimension (LDD,M)
On entry, the leading P-by-M part of this array must
contain the system direct input/output transmission
matrix D.
On exit, if JOBD = 'D', the leading P-by-M part of this
array contains the direct input/output transmission
matrix Dc of the closed-loop system.
The array D is not referenced if JOBD = 'Z'.
LDD INTEGER
The leading dimension of array D.
LDD >= MAX(1,P) if JOBD = 'D'.
LDD >= 1 if JOBD = 'Z'.
F (input) DOUBLE PRECISION array, dimension (LDF,P)
If FBTYPE = 'O', the leading M-by-P part of this array
must contain the output feedback matrix F.
If FBTYPE = 'I', then the feedback matrix is assumed to be
an M x M order identity matrix.
The array F is not referenced if FBTYPE = 'I' or
ALPHA = 0.
LDF INTEGER
The leading dimension of array F.
LDF >= MAX(1,M) if FBTYPE = 'O' and ALPHA <> 0.
LDF >= 1 if FBTYPE = 'I' or ALPHA = 0.
RCOND (output) DOUBLE PRECISION
The reciprocal condition number of the matrix
I - alpha*D*F.
</PRE>
<B>Workspace</B>
<PRE>
IWORK INTEGER array, dimension (LIWORK)
LIWORK >= MAX(1,2*P) if JOBD = 'D'.
LIWORK >= 1 if JOBD = 'Z'.
IWORK is not referenced if JOBD = 'Z'.
DWORK DOUBLE PRECISION array, dimension (LDWORK)
LDWORK INTEGER
The length of the array DWORK.
LDWORK >= wspace, where
wspace = MAX( 1, M, P*P + 4*P ) if JOBD = 'D',
wspace = MAX( 1, M ) if JOBD = 'Z'.
For best performance, LDWORK >= MAX( wspace, N*M, N*P ).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value;
= 1: if the matrix I - alpha*D*F is numerically singular.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The matrices of the closed-loop system have the expressions:
Ac = A + alpha*B*F*E*C, Bc = B + alpha*B*F*E*D,
Cc = E*C, Dc = E*D,
where E = (I - alpha*D*F)**-1.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The accuracy of computations basically depends on the conditioning
of the matrix I - alpha*D*F. If RCOND is very small, it is likely
that the computed results are inaccurate.
</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>
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