SB10WD

H2 optimal controller matrices using state feedback and output injection matrices (continuous-time)

Purpose

  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.

      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, * )

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. 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).

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  The routine implements the formulas given in [1], [2].

  [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.

  The accuracy of the result depends on the condition numbers of the
  input and output transformations.

  None

Program Text

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