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SUBROUTINE SB10KD( N, M, NP, A, LDA, B, LDB, C, LDC, FACTOR,
$ AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK, RCOND,
$ IWORK, DWORK, LDWORK, BWORK, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To compute the matrices of the positive feedback controller
C
C | Ak | Bk |
C K = |----|----|
C | Ck | Dk |
C
C for the shaped plant
C
C | A | B |
C G = |---|---|
C | C | 0 |
C
C in the Discrete-Time Loop Shaping Design Procedure.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C N (input) INTEGER
C The order of the plant. N >= 0.
C
C M (input) INTEGER
C The column size of the matrix B. M >= 0.
C
C NP (input) INTEGER
C The row size of the matrix C. NP >= 0.
C
C A (input) DOUBLE PRECISION array, dimension (LDA,N)
C The leading N-by-N part of this array must contain the
C system state matrix A of the shaped plant.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= max(1,N).
C
C B (input) DOUBLE PRECISION array, dimension (LDB,M)
C The leading N-by-M part of this array must contain the
C system input matrix B of the shaped plant.
C
C LDB INTEGER
C The leading dimension of the array B. LDB >= max(1,N).
C
C C (input) DOUBLE PRECISION array, dimension (LDC,N)
C The leading NP-by-N part of this array must contain the
C system output matrix C of the shaped plant.
C
C LDC INTEGER
C The leading dimension of the array C. LDC >= max(1,NP).
C
C FACTOR (input) DOUBLE PRECISION
C = 1 implies that an optimal controller is required;
C > 1 implies that a suboptimal controller is required
C achieving a performance FACTOR less than optimal.
C FACTOR >= 1.
C
C AK (output) DOUBLE PRECISION array, dimension (LDAK,N)
C The leading N-by-N part of this array contains the
C controller state matrix Ak.
C
C LDAK INTEGER
C The leading dimension of the array AK. LDAK >= max(1,N).
C
C BK (output) DOUBLE PRECISION array, dimension (LDBK,NP)
C The leading N-by-NP part of this array contains the
C controller input matrix Bk.
C
C LDBK INTEGER
C The leading dimension of the array BK. LDBK >= max(1,N).
C
C CK (output) DOUBLE PRECISION array, dimension (LDCK,N)
C The leading M-by-N part of this array contains the
C controller output matrix Ck.
C
C LDCK INTEGER
C The leading dimension of the array CK. LDCK >= max(1,M).
C
C DK (output) DOUBLE PRECISION array, dimension (LDDK,NP)
C The leading M-by-NP part of this array contains the
C controller matrix Dk.
C
C LDDK INTEGER
C The leading dimension of the array DK. LDDK >= max(1,M).
C
C RCOND (output) DOUBLE PRECISION array, dimension (4)
C RCOND(1) contains an estimate of the reciprocal condition
C number of the linear system of equations from
C which the solution of the P-Riccati equation is
C obtained;
C RCOND(2) contains an estimate of the reciprocal condition
C number of the linear system of equations from
C which the solution of the Q-Riccati equation is
C obtained;
C RCOND(3) contains an estimate of the reciprocal condition
C number of the linear system of equations from
C which the solution of the X-Riccati equation is
C obtained;
C RCOND(4) contains an estimate of the reciprocal condition
C number of the matrix Rx + Bx'*X*Bx (see the
C comments in the code).
C
C Workspace
C
C IWORK INTEGER array, dimension 2*max(N,NP+M)
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C On exit, if INFO = 0, DWORK(1) contains the optimal value
C of LDWORK.
C
C LDWORK INTEGER
C The dimension of the array DWORK.
C LDWORK >= 15*N*N + 6*N +
C max( 14*N+23, 16*N, 2*N+NP+M, 3*(NP+M) ) +
C max( N*N, 11*N*NP + 2*M*M + 8*NP*NP + 8*M*N +
C 4*M*NP + NP ).
C For good performance, LDWORK must generally be larger.
C
C BWORK LOGICAL array, dimension (2*N)
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value;
C = 1: the P-Riccati equation is not solved successfully;
C = 2: the Q-Riccati equation is not solved successfully;
C = 3: the X-Riccati equation is not solved successfully;
C = 4: the iteration to compute eigenvalues failed to
C converge;
C = 5: the matrix Rx + Bx'*X*Bx is singular;
C = 6: the closed-loop system is unstable.
C
C METHOD
C
C The routine implements the method presented in [1].
C
C REFERENCES
C
C [1] McFarlane, D. and Glover, K.
C A loop shaping design procedure using H_infinity synthesis.
C IEEE Trans. Automat. Control, vol. AC-37, no. 6, pp. 759-769,
C 1992.
C
C NUMERICAL ASPECTS
C
C The accuracy of the results depends on the conditioning of the
C two Riccati equations solved in the controller design. For
C better conditioning it is advised to take FACTOR > 1.
C
C CONTRIBUTORS
C
C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, October 2000.
C
C REVISIONS
C
C V. Sima, Katholieke University Leuven, January 2001,
C February 2001.
C
C KEYWORDS
C
C H_infinity control, Loop-shaping design, Robust control.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
C ..
C .. Scalar Arguments ..
INTEGER INFO, LDA, LDAK, LDB, LDBK, LDC, LDCK, LDDK,
$ LDWORK, M, N, NP
DOUBLE PRECISION FACTOR
C ..
C .. Array Arguments ..
INTEGER IWORK( * )
LOGICAL BWORK( * )
DOUBLE PRECISION A( LDA, * ), AK( LDAK, * ), B( LDB, * ),
$ BK( LDBK, * ), C( LDC, * ), CK( LDCK, * ),
$ DK( LDDK, * ), DWORK( * ), RCOND( 4 )
C ..
C .. Local Scalars ..
INTEGER I, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10,
$ I11, I12, I13, I14, I15, I16, I17, I18, I19,
$ I20, I21, I22, I23, I24, I25, I26, INFO2,
$ IWRK, J, LWA, LWAMAX, MINWRK, N2, NS, SDIM
DOUBLE PRECISION GAMMA, RNORM
C ..
C .. External Functions ..
LOGICAL SELECT
DOUBLE PRECISION DLANSY, DLAPY2
EXTERNAL DLANSY, DLAPY2, SELECT
C ..
C .. External Subroutines ..
EXTERNAL DGEMM, DGEES, DLACPY, DLASET, DPOTRF, DPOTRS,
$ DSYCON, DSYEV, DSYRK, DSYTRF, DSYTRS, SB02OD,
$ XERBLA
C ..
C .. Intrinsic Functions ..
INTRINSIC DBLE, INT, MAX, SQRT
C ..
C .. Executable Statements ..
C
C Decode and Test input parameters.
C
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( M.LT.0 ) THEN
INFO = -2
ELSE IF( NP.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDC.LT.MAX( 1, NP ) ) THEN
INFO = -9
ELSE IF( FACTOR.LT.ONE ) THEN
INFO = -10
ELSE IF( LDAK.LT.MAX( 1, N ) ) THEN
INFO = -12
ELSE IF( LDBK.LT.MAX( 1, N ) ) THEN
INFO = -14
ELSE IF( LDCK.LT.MAX( 1, M ) ) THEN
INFO = -16
ELSE IF( LDDK.LT.MAX( 1, M ) ) THEN
INFO = -18
END IF
C
C Compute workspace.
C
MINWRK = 15*N*N + 6*N + MAX( 14*N+23, 16*N, 2*N+NP+M, 3*(NP+M) ) +
$ MAX( N*N, 11*N*NP + 2*M*M + 8*NP*NP + 8*M*N +
$ 4*M*NP + NP )
IF( LDWORK.LT.MINWRK ) THEN
INFO = -22
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SB10KD', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 ) THEN
RCOND( 1 ) = ONE
RCOND( 2 ) = ONE
RCOND( 3 ) = ONE
RCOND( 4 ) = ONE
DWORK( 1 ) = ONE
RETURN
END IF
C
C Workspace usage.
C
N2 = 2*N
I1 = N*N
I2 = I1 + N*N
I3 = I2 + N*N
I4 = I3 + N*N
I5 = I4 + N2
I6 = I5 + N2
I7 = I6 + N2
I8 = I7 + N2*N2
I9 = I8 + N2*N2
C
IWRK = I9 + N2*N2
LWAMAX = 0
C
C Compute Cr = C'*C .
C
CALL DSYRK( 'U', 'T', N, NP, ONE, C, LDC, ZERO, DWORK( I2+1 ), N )
C
C Compute Dr = B*B' .
C
CALL DSYRK( 'U', 'N', N, M, ONE, B, LDB, ZERO, DWORK( I3+1 ), N )
C -1
C Solution of the Riccati equation A'*P*(In + Dr*P) *A - P + Cr = 0.
C
CALL SB02OD( 'D', 'G', 'N', 'U', 'Z', 'S', N, M, NP, A, LDA,
$ DWORK( I3+1 ), N, DWORK( I2+1 ), N, DWORK, M, DWORK,
$ N, RCOND( 1 ), DWORK, N, DWORK( I4+1 ),
$ DWORK( I5+1 ), DWORK( I6+1 ), DWORK( I7+1 ), N2,
$ DWORK( I8+1 ), N2, DWORK( I9+1 ), N2, -ONE, IWORK,
$ DWORK( IWRK+1 ), LDWORK-IWRK, BWORK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 1
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
C
C Transpose A in AK (used as workspace).
C
DO 40 J = 1, N
DO 30 I = 1, N
AK( I,J ) = A( J,I )
30 CONTINUE
40 CONTINUE
C -1
C Solution of the Riccati equation A*Q*(In + Cr*Q) *A' - Q + Dr = 0.
C
CALL SB02OD( 'D', 'G', 'N', 'U', 'Z', 'S', N, M, NP, AK, LDAK,
$ DWORK( I2+1 ), N, DWORK( I3+1 ), N, DWORK, M, DWORK,
$ N, RCOND( 2 ), DWORK( I1+1 ), N, DWORK( I4+1 ),
$ DWORK( I5+1 ), DWORK( I6+1 ), DWORK( I7+1 ), N2,
$ DWORK( I8+1 ), N2, DWORK( I9+1 ), N2, -ONE, IWORK,
$ DWORK( IWRK+1 ), LDWORK-IWRK, BWORK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 2
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
C
C Compute gamma.
C
CALL DGEMM( 'N', 'N', N, N, N, ONE, DWORK( I1+1 ), N, DWORK, N,
$ ZERO, AK, LDAK )
CALL DGEES( 'N', 'N', SELECT, N, AK, LDAK, SDIM, DWORK( I6+1 ),
$ DWORK( I7+1 ), DWORK( IWRK+1 ), N, DWORK( IWRK+1 ),
$ LDWORK-IWRK, BWORK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 4
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
GAMMA = ZERO
DO 50 I = 1, N
GAMMA = MAX( GAMMA, DWORK( I6+I ) )
50 CONTINUE
GAMMA = FACTOR*SQRT( ONE + GAMMA )
C
C Workspace usage.
C
I3 = I2 + N*NP
I4 = I3 + NP*NP
I5 = I4 + NP*NP
I6 = I5 + NP*NP
I7 = I6 + NP
I8 = I7 + NP*NP
I9 = I8 + NP*NP
I10 = I9 + NP*NP
I11 = I10 + N*NP
I12 = I11 + N*NP
I13 = I12 + ( NP+M )*( NP+M )
I14 = I13 + N*( NP+M )
I15 = I14 + N*( NP+M )
I16 = I15 + N*N
I17 = I16 + N2
I18 = I17 + N2
I19 = I18 + N2
I20 = I19 + ( N2+NP+M )*( N2+NP+M )
I21 = I20 + ( N2+NP+M )*N2
C
IWRK = I21 + N2*N2
C
C Compute Q*C' .
C
CALL DGEMM( 'N', 'T', N, NP, N, ONE, DWORK( I1+1 ), N, C, LDC,
$ ZERO, DWORK( I2+1 ), N )
C
C Compute Ip + C*Q*C' .
C
CALL DLASET( 'Full', NP, NP, ZERO, ONE, DWORK( I3+1 ), NP )
CALL DGEMM( 'N', 'N', NP, NP, N, ONE, C, LDC, DWORK( I2+1 ), N,
$ ONE, DWORK( I3+1 ), NP )
C
C Compute the eigenvalues and eigenvectors of Ip + C'*Q*C
C
CALL DLACPY( 'U', NP, NP, DWORK( I3+1 ), NP, DWORK( I5+1 ), NP )
CALL DSYEV( 'V', 'U', NP, DWORK( I5+1 ), NP, DWORK( I6+1 ),
$ DWORK( IWRK+1 ), LDWORK-IWRK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 4
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
C -1
C Compute ( Ip + C'*Q*C ) .
C
DO 70 J = 1, NP
DO 60 I = 1, NP
DWORK( I9+I+(J-1)*NP ) = DWORK( I5+J+(I-1)*NP ) /
$ DWORK( I6+I )
60 CONTINUE
70 CONTINUE
CALL DGEMM( 'N', 'N', NP, NP, NP, ONE, DWORK( I5+1 ), NP,
$ DWORK( I9+1 ), NP, ZERO, DWORK( I4+1 ), NP )
C
C Compute Z2 .
C
DO 90 J = 1, NP
DO 80 I = 1, NP
DWORK( I9+I+(J-1)*NP ) = DWORK( I5+J+(I-1)*NP ) /
$ SQRT( DWORK( I6+I ) )
80 CONTINUE
90 CONTINUE
CALL DGEMM( 'N', 'N', NP, NP, NP, ONE, DWORK( I5+1 ), NP,
$ DWORK( I9+1 ), NP, ZERO, DWORK( I7+1 ), NP )
C -1
C Compute Z2 .
C
DO 110 J = 1, NP
DO 100 I = 1, NP
DWORK( I9+I+(J-1)*NP ) = DWORK( I5+J+(I-1)*NP )*
$ SQRT( DWORK( I6+I ) )
100 CONTINUE
110 CONTINUE
CALL DGEMM( 'N', 'N', NP, NP, NP, ONE, DWORK( I5+1 ), NP,
$ DWORK( I9+1 ), NP, ZERO, DWORK( I8+1 ), NP )
C
C Compute A*Q*C' .
C
CALL DGEMM( 'N', 'N', N, NP, N, ONE, A, LDA, DWORK( I2+1 ), N,
$ ZERO, DWORK( I10+1 ), N )
C -1
C Compute H = -A*Q*C'*( Ip + C*Q*C' ) .
C
CALL DGEMM( 'N', 'N', N, NP, NP, -ONE, DWORK( I10+1 ), N,
$ DWORK( I4+1 ), NP, ZERO, DWORK( I11+1 ), N )
C
C Compute Rx .
C
CALL DLASET( 'F', NP+M, NP+M, ZERO, ONE, DWORK( I12+1 ), NP+M )
DO 130 J = 1, NP
DO 120 I = 1, NP
DWORK( I12+I+(J-1)*(NP+M) ) = DWORK( I3+I+(J-1)*NP )
120 CONTINUE
DWORK( I12+J+(J-1)*(NP+M) ) = DWORK( I3+J+(J-1)*NP ) -
$ GAMMA*GAMMA
130 CONTINUE
C
C Compute Bx .
C
CALL DGEMM( 'N', 'N', N, NP, NP, -ONE, DWORK( I11+1 ), N,
$ DWORK( I8+1 ), NP, ZERO, DWORK( I13+1 ), N )
DO 150 J = 1, M
DO 140 I = 1, N
DWORK( I13+N*NP+I+(J-1)*N ) = B( I, J )
140 CONTINUE
150 CONTINUE
C
C Compute Sx .
C
CALL DGEMM( 'T', 'N', N, NP, NP, ONE, C, LDC, DWORK( I8+1 ), NP,
$ ZERO, DWORK( I14+1 ), N )
CALL DLASET( 'F', N, M, ZERO, ZERO, DWORK( I14+N*NP+1 ), N )
C
C Solve the Riccati equation
C -1
C X = A'*X*A + Cx - (Sx + A'*X*Bx)*(Rx + Bx'*X*B ) *(Sx'+Bx'*X*A).
C
CALL SB02OD( 'D', 'B', 'C', 'U', 'N', 'S', N, NP+M, NP, A, LDA,
$ DWORK( I13+1 ), N, C, LDC, DWORK( I12+1 ), NP+M,
$ DWORK( I14+1 ), N, RCOND( 3 ), DWORK( I15+1 ), N,
$ DWORK( I16+1 ), DWORK( I17+1 ), DWORK( I18+1 ),
$ DWORK( I19+1 ), N2+NP+M, DWORK( I20+1 ), N2+NP+M,
$ DWORK( I21+1 ), N2, -ONE, IWORK, DWORK( IWRK+1 ),
$ LDWORK-IWRK, BWORK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 3
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
C
I22 = I16
I23 = I22 + ( NP+M )*N
I24 = I23 + ( NP+M )*( NP+M )
I25 = I24 + ( NP+M )*N
I26 = I25 + M*N
C
IWRK = I25
C
C Compute Bx'*X .
C
CALL DGEMM( 'T', 'N', NP+M, N, N, ONE, DWORK( I13+1 ), N,
$ DWORK( I15+1 ), N, ZERO, DWORK( I22+1 ), NP+M )
C
C Compute Rx + Bx'*X*Bx .
C
CALL DLACPY( 'F', NP+M, NP+M, DWORK( I12+1 ), NP+M,
$ DWORK( I23+1 ), NP+M )
CALL DGEMM( 'N', 'N', NP+M, NP+M, N, ONE, DWORK( I22+1 ), NP+M,
$ DWORK( I13+1 ), N, ONE, DWORK( I23+1 ), NP+M )
C
C Compute -( Sx' + Bx'*X*A ) .
C
DO 170 J = 1, N
DO 160 I = 1, NP+M
DWORK( I24+I+(J-1)*(NP+M) ) = DWORK( I14+J+(I-1)*N )
160 CONTINUE
170 CONTINUE
CALL DGEMM( 'N', 'N', NP+M, N, N, -ONE, DWORK( I22+1 ), NP+M,
$ A, LDA, -ONE, DWORK( I24+1 ), NP+M )
C
C Factorize Rx + Bx'*X*Bx .
C
RNORM = DLANSY( '1', 'U', NP+M, DWORK( I23+1 ), NP+M,
$ DWORK( IWRK+1 ) )
CALL DSYTRF( 'U', NP+M, DWORK( I23+1 ), NP+M, IWORK,
$ DWORK( IWRK+1 ), LDWORK-IWRK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 5
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
CALL DSYCON( 'U', NP+M, DWORK( I23+1 ), NP+M, IWORK, RNORM,
$ RCOND( 4 ), DWORK( IWRK+1 ), IWORK( NP+M+1), INFO2 )
C -1
C Compute F = -( Rx + Bx'*X*Bx ) ( Sx' + Bx'*X*A ) .
C
CALL DSYTRS( 'U', NP+M, N, DWORK( I23+1 ), NP+M, IWORK,
$ DWORK( I24+1 ), NP+M, INFO2 )
C
C Compute B'*X .
C
CALL DGEMM( 'T', 'N', M, N, N, ONE, B, LDB, DWORK( I15+1 ), N,
$ ZERO, DWORK( I25+1 ), M )
C
C Compute Im + B'*X*B .
C
CALL DLASET( 'F', M, M, ZERO, ONE, DWORK( I23+1 ), M )
CALL DGEMM( 'N', 'N', M, M, N, ONE, DWORK( I25+1 ), M, B, LDB,
$ ONE, DWORK( I23+1 ), M )
C
C Factorize Im + B'*X*B .
C
CALL DPOTRF( 'U', M, DWORK( I23+1 ), M, INFO2 )
C -1
C Compute ( Im + B'*X*B ) B'*X .
C
CALL DPOTRS( 'U', M, N, DWORK( I23+1 ), M, DWORK( I25+1 ), M,
$ INFO2 )
C -1
C Compute Dk = ( Im + B'*X*B ) B'*X*H .
C
CALL DGEMM( 'N', 'N', M, NP, N, ONE, DWORK( I25+1 ), M,
$ DWORK( I11+1 ), N, ZERO, DK, LDDK )
C
C Compute Bk = -H + B*Dk .
C
CALL DLACPY( 'F', N, NP, DWORK( I11+1 ), N, BK, LDBK )
CALL DGEMM( 'N', 'N', N, NP, M, ONE, B, LDB, DK, LDDK, -ONE,
$ BK, LDBK )
C -1
C Compute Dk*Z2 .
C
CALL DGEMM( 'N', 'N', M, NP, NP, ONE, DK, LDDK, DWORK( I8+1 ),
$ NP, ZERO, DWORK( I26+1 ), M )
C
C Compute F1 + Z2*C .
C
CALL DLACPY( 'F', NP, N, DWORK( I24+1 ), NP+M, DWORK( I12+1 ),
$ NP )
CALL DGEMM( 'N', 'N', NP, N, NP, ONE, DWORK( I7+1 ), NP, C, LDC,
$ ONE, DWORK( I12+1 ), NP )
C -1
C Compute Ck = F2 - Dk*Z2 *( F1 + Z2*C ) .
C
CALL DLACPY( 'F', M, N, DWORK( I24+NP+1 ), NP+M, CK, LDCK )
CALL DGEMM( 'N', 'N', M, N, NP, -ONE, DWORK( I26+1 ), M,
$ DWORK( I12+1 ), NP, ONE, CK, LDCK )
C
C Compute Ak = A + H*C + B*Ck .
C
CALL DLACPY( 'F', N, N, A, LDA, AK, LDAK )
CALL DGEMM( 'N', 'N', N, N, NP, ONE, DWORK( I11+1 ), N, C, LDC,
$ ONE, AK, LDAK )
CALL DGEMM( 'N', 'N', N, N, M, ONE, B, LDB, CK, LDCK, ONE, AK,
$ LDAK )
C
C Workspace usage.
C
I1 = M*N
I2 = I1 + N2*N2
I3 = I2 + N2
C
IWRK = I3 + N2
C
C Compute Dk*C .
C
CALL DGEMM( 'N', 'N', M, N, NP, ONE, DK, LDDK, C, LDC, ZERO,
$ DWORK, M )
C
C Compute the closed-loop state matrix.
C
CALL DLACPY( 'F', N, N, A, LDA, DWORK( I1+1 ), N2 )
CALL DGEMM( 'N', 'N', N, N, M, -ONE, B, LDB, DWORK, M, ONE,
$ DWORK( I1+1 ), N2 )
CALL DGEMM( 'N', 'N', N, N, NP, -ONE, BK, LDBK, C, LDC, ZERO,
$ DWORK( I1+N+1 ), N2 )
CALL DGEMM( 'N', 'N', N, N, M, ONE, B, LDB, CK, LDCK, ZERO,
$ DWORK( I1+N2*N+1 ), N2 )
CALL DLACPY( 'F', N, N, AK, LDAK, DWORK( I1+N2*N+N+1 ), N2 )
C
C Compute the closed-loop poles.
C
CALL DGEES( 'N', 'N', SELECT, N2, DWORK( I1+1 ), N2, SDIM,
$ DWORK( I2+1 ), DWORK( I3+1 ), DWORK( IWRK+1 ), N,
$ DWORK( IWRK+1 ), LDWORK-IWRK, BWORK, INFO2 )
IF( INFO2.NE.0 ) THEN
INFO = 4
RETURN
END IF
LWA = INT( DWORK( IWRK+1 ) ) + IWRK
LWAMAX = MAX( LWA, LWAMAX )
C
C Check the stability of the closed-loop system.
C
NS = 0
DO 180 I = 1, N2
IF( DLAPY2( DWORK( I2+I ), DWORK( I3+I ) ).GT.ONE ) NS = NS + 1
180 CONTINUE
IF( NS.GT.0 ) THEN
INFO = 6
RETURN
END IF
C
DWORK( 1 ) = DBLE( LWAMAX )
RETURN
C *** Last line of SB10KD ***
END
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