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<HTML>
<HEAD><TITLE>SB10WD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="SB10WD">SB10WD</A></H2>
<H3>
H2 optimal controller matrices using state feedback and output injection matrices (continuous-time)
</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 matrices of the H2 optimal controller
| AK | BK |
K = |----|----|,
| CK | DK |
from the state feedback matrix F and output injection matrix H as
determined by the SLICOT Library routine SB10VD.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE SB10WD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC,
$ D, LDD, F, LDF, H, LDH, TU, LDTU, TY, LDTY,
$ AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDA, LDAK, LDB, LDBK, LDC, LDCK, LDD,
$ LDDK, LDF, LDH, LDTU, LDTY, M, N, NCON, NMEAS,
$ NP
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), AK( LDAK, * ), B( LDB, * ),
$ BK( LDBK, * ), C( LDC, * ), CK( LDCK, * ),
$ D( LDD, * ), DK( LDDK, * ), F( LDF, * ),
$ H( LDH, * ), TU( LDTU, * ), TY( LDTY, * )
</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 system. N >= 0.
M (input) INTEGER
The column size of the matrix B. M >= 0.
NP (input) INTEGER
The row size of the matrix C. NP >= 0.
NCON (input) INTEGER
The number of control inputs (M2). M >= NCON >= 0.
NP-NMEAS >= NCON.
NMEAS (input) INTEGER
The number of measurements (NP2). NP >= NMEAS >= 0.
M-NCON >= NMEAS.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The leading N-by-N part of this array must contain the
system state matrix A.
LDA INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) DOUBLE PRECISION array, dimension (LDB,M)
The leading N-by-M part of this array must contain the
system input matrix B. Only the submatrix
B2 = B(:,M-M2+1:M) is used.
LDB INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C (input) DOUBLE PRECISION array, dimension (LDC,N)
The leading NP-by-N part of this array must contain the
system output matrix C. Only the submatrix
C2 = C(NP-NP2+1:NP,:) is used.
LDC INTEGER
The leading dimension of the array C. LDC >= max(1,NP).
D (input) DOUBLE PRECISION array, dimension (LDD,M)
The leading NP-by-M part of this array must contain the
system input/output matrix D. Only the submatrix
D22 = D(NP-NP2+1:NP,M-M2+1:M) is used.
LDD INTEGER
The leading dimension of the array D. LDD >= max(1,NP).
F (input) DOUBLE PRECISION array, dimension (LDF,N)
The leading NCON-by-N part of this array must contain the
state feedback matrix F.
LDF INTEGER
The leading dimension of the array F. LDF >= max(1,NCON).
H (input) DOUBLE PRECISION array, dimension (LDH,NMEAS)
The leading N-by-NMEAS part of this array must contain the
output injection matrix H.
LDH INTEGER
The leading dimension of the array H. LDH >= max(1,N).
TU (input) DOUBLE PRECISION array, dimension (LDTU,M2)
The leading M2-by-M2 part of this array must contain the
control transformation matrix TU, as obtained by the
SLICOT Library routine SB10UD.
LDTU INTEGER
The leading dimension of the array TU. LDTU >= max(1,M2).
TY (input) DOUBLE PRECISION array, dimension (LDTY,NP2)
The leading NP2-by-NP2 part of this array must contain the
measurement transformation matrix TY, as obtained by the
SLICOT Library routine SB10UD.
LDTY INTEGER
The leading dimension of the array TY.
LDTY >= max(1,NP2).
AK (output) DOUBLE PRECISION array, dimension (LDAK,N)
The leading N-by-N part of this array contains the
controller state matrix AK.
LDAK INTEGER
The leading dimension of the array AK. LDAK >= max(1,N).
BK (output) DOUBLE PRECISION array, dimension (LDBK,NMEAS)
The leading N-by-NMEAS part of this array contains the
controller input matrix BK.
LDBK INTEGER
The leading dimension of the array BK. LDBK >= max(1,N).
CK (output) DOUBLE PRECISION array, dimension (LDCK,N)
The leading NCON-by-N part of this array contains the
controller output matrix CK.
LDCK INTEGER
The leading dimension of the array CK.
LDCK >= max(1,NCON).
DK (output) DOUBLE PRECISION array, dimension (LDDK,NMEAS)
The leading NCON-by-NMEAS part of this array contains the
controller input/output matrix DK.
LDDK INTEGER
The leading dimension of the array DK.
LDDK >= max(1,NCON).
</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 routine implements the formulas given in [1], [2].
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Zhou, K., Doyle, J.C., and Glover, K.
Robust and Optimal Control.
Prentice-Hall, Upper Saddle River, NJ, 1996.
[2] Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and
Smith, R.
mu-Analysis and Synthesis Toolbox.
The MathWorks Inc., Natick, Mass., 1995.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The accuracy of the result depends on the condition numbers of the
input and output transformations.
</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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