SB10WD - SLICOT Library Routine Documentation

## SB10WD

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

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

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.

Specification

          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, * )

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. 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).

Error Indicator

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

Method

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

References

      [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.

Numerical Aspects

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

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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