## SB10LD

### Closed-loop system matrices for a system with robust controller

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To compute the matrices of the closed-loop system

| AC | BC |
G = |----|----|,
| CC | DC |

from the matrices of the open-loop system

| A | B |
P = |---|---|
| C | D |

and the matrices of the controller

| AK | BK |
K = |----|----|.
| CK | DK |

```
Specification
```      SUBROUTINE SB10LD( N, M, NP, NCON, NMEAS, A, LDA, B, LDB, C, LDC,
\$                   D, LDD, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK,
\$                   AC, LDAC, BC, LDBC, CC, LDCC, DC, LDDC, IWORK,
\$                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
INTEGER            INFO, LDA, LDAC, LDAK, LDB, LDBC, LDBK, LDC,
\$                   LDCC, LDCK, LDD, LDDC, LDDK, LDWORK, M, N,
\$                   NCON, NMEAS, NP
C     .. Array Arguments ..
INTEGER            IWORK( * )
DOUBLE PRECISION   A( LDA, * ), AC( LDAC, * ), AK( LDAK, * ),
\$                   B( LDB, * ), BC( LDBC, * ), BK( LDBK, * ),
\$                   C( LDC, * ), CC( LDCC, * ), CK( LDCK, * ),
\$                   D( LDD, * ), DC( LDDC, * ), DK( LDDK, * ),
\$                   DWORK( * )

```
Arguments

Input/Output Parameters

```  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.

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.

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.

LDD     INTEGER
The leading dimension of the array D.  LDD >= max(1,NP).

AK      (input) DOUBLE PRECISION array, dimension (LDAK,N)
The leading N-by-N part of this array must contain the
controller state matrix AK.

LDAK    INTEGER
The leading dimension of the array AK.  LDAK >= max(1,N).

BK      (input) DOUBLE PRECISION array, dimension (LDBK,NMEAS)
The leading N-by-NMEAS part of this array must contain the
controller input matrix BK.

LDBK    INTEGER
The leading dimension of the array BK.  LDBK >= max(1,N).

CK      (input) DOUBLE PRECISION array, dimension (LDCK,N)
The leading NCON-by-N part of this array must contain the
controller output matrix CK.

LDCK    INTEGER
The leading dimension of the array CK.
LDCK >= max(1,NCON).

DK      (input) DOUBLE PRECISION array, dimension (LDDK,NMEAS)
The leading NCON-by-NMEAS part of this array must contain
the controller input/output matrix DK.

LDDK    INTEGER
The leading dimension of the array DK.
LDDK >= max(1,NCON).

AC      (output) DOUBLE PRECISION array, dimension (LDAC,2*N)
The leading 2*N-by-2*N part of this array contains the
closed-loop system state matrix AC.

LDAC    INTEGER
The leading dimension of the array AC.
LDAC >= max(1,2*N).

BC      (output) DOUBLE PRECISION array, dimension (LDBC,M-NCON)
The leading 2*N-by-(M-NCON) part of this array contains
the closed-loop system input matrix BC.

LDBC    INTEGER
The leading dimension of the array BC.
LDBC >= max(1,2*N).

CC      (output) DOUBLE PRECISION array, dimension (LDCC,2*N)
The leading (NP-NMEAS)-by-2*N part of this array contains
the closed-loop system output matrix CC.

LDCC    INTEGER
The leading dimension of the array CC.
LDCC >= max(1,NP-NMEAS).

DC      (output) DOUBLE PRECISION array, dimension (LDDC,M-NCON)
The leading (NP-NMEAS)-by-(M-NCON) part of this array
contains the closed-loop system input/output matrix DC.

LDDC    INTEGER
The leading dimension of the array DC.
LDDC >= max(1,NP-NMEAS).

```
Workspace
```  IWORK   INTEGER array, dimension (2*max(NCON,NMEAS))

DWORK   DOUBLE PRECISION array, dimension (LDWORK)
On exit, if INFO = 0, DWORK(1) contains the optimal
LDWORK.

LDWORK  INTEGER
The dimension of the array DWORK.
LDWORK >= 2*M*M+NP*NP+2*M*N+M*NP+2*N*NP.
For good performance, LDWORK must generally be larger.

Error Indicactor

INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value;
= 1:  if the matrix Inp2 - D22*DK is singular to working
precision;
= 2:  if the matrix Im2 - DK*D22 is singular to working
precision.

```
Method
```  The routine implements the formulas given in .

```
References
```   Balas, G.J., Doyle, J.C., Glover, K., Packard, A., and
Smith, R.
mu-Analysis and Synthesis Toolbox.
The MathWorks Inc., Natick, Mass., 1995.

```
Numerical Aspects
```  The accuracy of the result depends on the condition numbers of the
matrices  Inp2 - D22*DK  and  Im2 - DK*D22.

```
```  None
```
Example

Program Text

```  None
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Program Data
```  None
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Program Results
```  None
```