351 lines
11 KiB
Fortran
351 lines
11 KiB
Fortran
SUBROUTINE SB10TD( N, M, NP, NCON, NMEAS, D, LDD, TU, LDTU, TY,
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$ LDTY, AK, LDAK, BK, LDBK, CK, LDCK, DK, LDDK,
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$ RCOND, TOL, IWORK, DWORK, LDWORK, INFO )
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C
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C SLICOT RELEASE 5.0.
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C
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C Copyright (c) 2002-2009 NICONET e.V.
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C
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C This program is free software: you can redistribute it and/or
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C modify it under the terms of the GNU General Public License as
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C published by the Free Software Foundation, either version 2 of
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C the License, or (at your option) any later version.
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C
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C This program is distributed in the hope that it will be useful,
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C but WITHOUT ANY WARRANTY; without even the implied warranty of
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C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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C GNU General Public License for more details.
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C
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C You should have received a copy of the GNU General Public License
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C along with this program. If not, see
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C <http://www.gnu.org/licenses/>.
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C
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C PURPOSE
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C
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C To compute the matrices of the H2 optimal discrete-time controller
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C
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C | AK | BK |
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C K = |----|----|,
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C | CK | DK |
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C
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C from the matrices of the controller for the normalized system,
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C as determined by the SLICOT Library routine SB10SD.
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C
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C ARGUMENTS
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C
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C Input/Output Parameters
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C
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C N (input) INTEGER
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C The order of the system. N >= 0.
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C
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C M (input) INTEGER
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C The column size of the matrix B. M >= 0.
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C
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C NP (input) INTEGER
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C The row size of the matrix C. NP >= 0.
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C
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C NCON (input) INTEGER
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C The number of control inputs (M2). M >= NCON >= 0.
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C NP-NMEAS >= NCON.
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C
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C NMEAS (input) INTEGER
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C The number of measurements (NP2). NP >= NMEAS >= 0.
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C M-NCON >= NMEAS.
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C
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C D (input) DOUBLE PRECISION array, dimension (LDD,M)
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C The leading NP-by-M part of this array must contain the
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C system input/output matrix D. Only the trailing
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C NMEAS-by-NCON submatrix D22 is used.
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C
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C LDD INTEGER
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C The leading dimension of the array D. LDD >= max(1,NP).
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C
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C TU (input) DOUBLE PRECISION array, dimension (LDTU,M2)
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C The leading M2-by-M2 part of this array must contain the
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C control transformation matrix TU, as obtained by the
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C SLICOT Library routine SB10PD.
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C
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C LDTU INTEGER
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C The leading dimension of the array TU. LDTU >= max(1,M2).
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C
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C TY (input) DOUBLE PRECISION array, dimension (LDTY,NP2)
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C The leading NP2-by-NP2 part of this array must contain the
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C measurement transformation matrix TY, as obtained by the
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C SLICOT Library routine SB10PD.
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C
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C LDTY INTEGER
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C The leading dimension of the array TY.
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C LDTY >= max(1,NP2).
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C
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C AK (input/output) DOUBLE PRECISION array, dimension (LDAK,N)
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C On entry, the leading N-by-N part of this array must
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C contain controller state matrix for the normalized system
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C as obtained by the SLICOT Library routine SB10SD.
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C On exit, the leading N-by-N part of this array contains
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C controller state matrix AK.
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C
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C LDAK INTEGER
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C The leading dimension of the array AK. LDAK >= max(1,N).
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C
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C BK (input/output) DOUBLE PRECISION array, dimension
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C (LDBK,NMEAS)
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C On entry, the leading N-by-NMEAS part of this array must
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C contain controller input matrix for the normalized system
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C as obtained by the SLICOT Library routine SB10SD.
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C On exit, the leading N-by-NMEAS part of this array
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C contains controller input matrix BK.
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C
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C LDBK INTEGER
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C The leading dimension of the array BK. LDBK >= max(1,N).
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C
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C CK (input/output) DOUBLE PRECISION array, dimension (LDCK,N)
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C On entry, the leading NCON-by-N part of this array must
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C contain controller output matrix for the normalized
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C system as obtained by the SLICOT Library routine SB10SD.
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C On exit, the leading NCON-by-N part of this array contains
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C controller output matrix CK.
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C
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C LDCK INTEGER
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C The leading dimension of the array CK.
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C LDCK >= max(1,NCON).
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C
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C DK (input/output) DOUBLE PRECISION array, dimension
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C (LDDK,NMEAS)
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C On entry, the leading NCON-by-NMEAS part of this array
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C must contain controller matrix DK for the normalized
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C system as obtained by the SLICOT Library routine SB10SD.
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C On exit, the leading NCON-by-NMEAS part of this array
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C contains controller input/output matrix DK.
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C
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C LDDK INTEGER
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C The leading dimension of the array DK.
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C LDDK >= max(1,NCON).
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C
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C RCOND (output) DOUBLE PRECISION
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C RCOND contains an estimate of the reciprocal condition
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C number of the matrix Im2 + DKHAT*D22 which must be
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C inverted in the computation of the controller.
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C
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C Tolerances
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C
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C TOL DOUBLE PRECISION
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C Tolerance used in determining the nonsingularity of the
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C matrix which must be inverted. If TOL <= 0, then a default
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C value equal to sqrt(EPS) is used, where EPS is the
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C relative machine precision.
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C
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C Workspace
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C
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C IWORK INTEGER array, dimension (2*M2)
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C
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C DWORK DOUBLE PRECISION array, dimension (LDWORK)
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C
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C LDWORK INTEGER
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C The dimension of the array DWORK.
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C LDWORK >= max(N*M2,N*NP2,M2*NP2,M2*M2+4*M2).
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C
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C Error Indicator
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C
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C INFO INTEGER
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C = 0: successful exit;
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C < 0: if INFO = -i, the i-th argument had an illegal
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C value;
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C = 1: if the matrix Im2 + DKHAT*D22 is singular, or the
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C estimated condition number is larger than or equal
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C to 1/TOL.
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C
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C METHOD
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C
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C The routine implements the formulas given in [1].
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C
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C REFERENCES
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C
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C [1] Zhou, K., Doyle, J.C., and Glover, K.
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C Robust and Optimal Control.
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C Prentice-Hall, Upper Saddle River, NJ, 1996.
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C
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C [2] Petkov, P.Hr., Gu, D.W., and Konstantinov, M.M.
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C Fortran 77 routines for Hinf and H2 design of linear
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C discrete-time control systems.
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C Report 99-8, Department of Engineering, Leicester University,
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C April 1999.
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C
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C NUMERICAL ASPECTS
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C
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C The accuracy of the result depends on the condition numbers of the
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C input and output transformations and of the matrix Im2 +
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C DKHAT*D22.
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C
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C CONTRIBUTORS
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C
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C P.Hr. Petkov, D.W. Gu and M.M. Konstantinov, April 1999.
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C
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C REVISIONS
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C
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C V. Sima, Research Institute for Informatics, Bucharest, May 1999,
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C Jan. 2000.
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C
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C KEYWORDS
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C
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C Algebraic Riccati equation, H2 optimal control, LQG, LQR, optimal
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C regulator, robust control.
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C
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C ******************************************************************
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C
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C .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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C ..
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C .. Scalar Arguments ..
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INTEGER INFO, LDAK, LDBK, LDCK, LDD, LDDK, LDTU, LDTY,
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$ LDWORK, M, N, NCON, NMEAS, NP
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DOUBLE PRECISION RCOND, TOL
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C ..
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C .. Array Arguments ..
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INTEGER IWORK( * )
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DOUBLE PRECISION AK( LDAK, * ), BK( LDBK, * ), CK( LDCK, * ),
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$ D( LDD, * ), DK( LDDK, * ), DWORK( * ),
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$ TU( LDTU, * ), TY( LDTY, * )
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C ..
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C .. Local Scalars ..
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INTEGER INFO2, IWRK, M1, M2, MINWRK, NP1, NP2
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DOUBLE PRECISION ANORM, TOLL
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C ..
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C .. External Functions
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DOUBLE PRECISION DLAMCH, DLANGE
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EXTERNAL DLAMCH, DLANGE
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C ..
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C .. External Subroutines ..
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EXTERNAL DGECON, DGEMM, DGETRF, DGETRS, DLACPY, DLASET,
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$ XERBLA
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C ..
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C .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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C ..
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C .. Executable Statements ..
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C
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C Decode and Test input parameters.
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C
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M1 = M - NCON
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M2 = NCON
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NP1 = NP - NMEAS
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NP2 = NMEAS
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C
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( M.LT.0 ) THEN
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INFO = -2
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ELSE IF( NP.LT.0 ) THEN
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INFO = -3
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ELSE IF( NCON.LT.0 .OR. M1.LT.0 .OR. M2.GT.NP1 ) THEN
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INFO = -4
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ELSE IF( NMEAS.LT.0 .OR. NP1.LT.0 .OR. NP2.GT.M1 ) THEN
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INFO = -5
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ELSE IF( LDD.LT.MAX( 1, NP ) ) THEN
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INFO = -7
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ELSE IF( LDTU.LT.MAX( 1, M2 ) ) THEN
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INFO = -9
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ELSE IF( LDTY.LT.MAX( 1, NP2 ) ) THEN
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INFO = -11
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ELSE IF( LDAK.LT.MAX( 1, N ) ) THEN
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INFO = -13
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ELSE IF( LDBK.LT.MAX( 1, N ) ) THEN
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INFO = -15
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ELSE IF( LDCK.LT.MAX( 1, M2 ) ) THEN
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INFO = -17
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ELSE IF( LDDK.LT.MAX( 1, M2 ) ) THEN
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INFO = -19
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ELSE
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C
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C Compute workspace.
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C
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MINWRK = MAX ( N*M2, N*NP2, M2*NP2, M2*( M2 + 4 ) )
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IF( LDWORK.LT.MINWRK )
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$ INFO = -24
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SB10TD', -INFO )
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RETURN
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END IF
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C
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C Quick return if possible.
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C
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IF( N.EQ.0 .OR. M.EQ.0 .OR. NP.EQ.0 .OR. M1.EQ.0 .OR. M2.EQ.0
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$ .OR. NP1.EQ.0 .OR. NP2.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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END IF
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C
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TOLL = TOL
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IF( TOLL.LE.ZERO ) THEN
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C
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C Set the default value of the tolerance for nonsingularity test.
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C
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TOLL = SQRT( DLAMCH( 'Epsilon' ) )
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END IF
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C
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C Find BKHAT .
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C
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CALL DGEMM( 'N', 'N', N, NP2, NP2, ONE, BK, LDBK, TY, LDTY, ZERO,
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$ DWORK, N )
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CALL DLACPY ('Full', N, NP2, DWORK, N, BK, LDBK )
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C
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C Find CKHAT .
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C
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CALL DGEMM( 'N', 'N', M2, N, M2, ONE, TU, LDTU, CK, LDCK, ZERO,
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$ DWORK, M2 )
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CALL DLACPY ('Full', M2, N, DWORK, M2, CK, LDCK )
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C
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C Compute DKHAT .
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C
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CALL DGEMM( 'N', 'N', M2, NP2, M2, ONE, TU, LDTU, DK, LDDK, ZERO,
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$ DWORK, M2 )
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CALL DGEMM( 'N', 'N', M2, NP2, NP2, ONE, DWORK, M2, TY, LDTY,
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$ ZERO, DK, LDDK )
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C
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C Compute Im2 + DKHAT*D22 .
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C
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IWRK = M2*M2 + 1
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CALL DLASET( 'Full', M2, M2, ZERO, ONE, DWORK, M2 )
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CALL DGEMM( 'N', 'N', M2, M2, NP2, ONE, DK, LDDK,
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$ D( NP1+1, M1+1 ), LDD, ONE, DWORK, M2 )
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ANORM = DLANGE( '1', M2, M2, DWORK, M2, DWORK( IWRK ) )
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CALL DGETRF( M2, M2, DWORK, M2, IWORK, INFO2 )
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IF( INFO2.GT.0 ) THEN
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INFO = 1
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RETURN
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END IF
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CALL DGECON( '1', M2, DWORK, M2, ANORM, RCOND, DWORK( IWRK ),
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$ IWORK( M2+1 ), INFO2 )
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C
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C Return if the matrix is singular to working precision.
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C
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IF( RCOND.LT.TOLL ) THEN
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INFO = 1
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RETURN
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END IF
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C
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C Compute CK .
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C
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CALL DGETRS( 'N', M2, N, DWORK, M2, IWORK, CK, LDCK, INFO2 )
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C
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C Compute DK .
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C
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CALL DGETRS( 'N', M2, NP2, DWORK, M2, IWORK, DK, LDDK, INFO2 )
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C
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C Compute AK .
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C
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CALL DGEMM( 'N', 'N', N, M2, NP2, ONE, BK, LDBK, D( NP1+1, M1+1 ),
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$ LDD, ZERO, DWORK, N )
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CALL DGEMM( 'N', 'N', N, N, M2, -ONE, DWORK, N, CK, LDCK, ONE, AK,
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$ LDAK )
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C
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C Compute BK .
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C
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CALL DGEMM( 'N', 'N', N, NP2, M2, -ONE, DWORK, N, DK, LDDK,
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$ ONE, BK, LDBK )
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RETURN
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C *** Last line of SB10TD ***
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END
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