SB08GD

State-space representation of a left coprime factorization

Purpose

  To construct the state-space representation for the system
  G = (A,B,C,D) from the factors Q = (AQR,BQ,CQR,DQ) and
  R = (AQR,BR,CQR,DR) of its left coprime factorization
                -1
           G = R  * Q,

  where G, Q and R are the corresponding transfer-function matrices.

      SUBROUTINE SB08GD( N, M, P, A, LDA, B, LDB, C, LDC, D, LDD, BR,
     $                   LDBR, DR, LDDR, IWORK, DWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, LDA, LDB, LDBR, LDC, LDD, LDDR, M, N, P
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA,*), B(LDB,*), BR(LDBR,*), C(LDC,*),
     $                  D(LDD,*), DR(LDDR,*), DWORK(*)
      INTEGER           IWORK(*)

Input/Output Parameters

  N       (input) INTEGER
          The order of the matrix A. Also the number of rows of the
          matrices B and BR and the number of columns of the matrix
          C. N represents the order of the systems Q and R.  N >= 0.

  M       (input) INTEGER
          The dimension of input vector, i.e. the number of columns
          of the matrices B and D.  M >= 0.

  P       (input) INTEGER
          The dimension of output vector, i.e. the number of rows of
          the matrices C, D and DR and the number of columns of the
          matrices BR and DR.  P >= 0.

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the leading N-by-N part of this array must
          contain the state dynamics matrix AQR of the systems
          Q and R.
          On exit, the leading N-by-N part of this array contains
          the state dynamics matrix of the system G.

  LDA     INTEGER
          The leading dimension of array A.  LDA >= MAX(1,N).

  B       (input/output) DOUBLE PRECISION array, dimension (LDB,M)
          On entry, the leading N-by-M part of this array must
          contain the input/state matrix BQ of the system Q.
          On exit, the leading N-by-M part of this array contains
          the input/state matrix of the system G.

  LDB     INTEGER
          The leading dimension of array B.  LDB >= MAX(1,N).

  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the leading P-by-N part of this array must
          contain the state/output matrix CQR of the systems
          Q and R.
          On exit, the leading P-by-N part of this array contains
          the state/output matrix of the system G.

  LDC     INTEGER
          The leading dimension of array C.  LDC >= MAX(1,P).

  D       (input/output) DOUBLE PRECISION array, dimension (LDD,M)
          On entry, the leading P-by-M part of this array must
          contain the input/output matrix DQ of the system Q.
          On exit, the leading P-by-M part of this array contains
          the input/output matrix of the system G.

  LDD     INTEGER
          The leading dimension of array D.  LDD >= MAX(1,P).

  BR      (input) DOUBLE PRECISION array, dimension (LDBR,P)
          The leading N-by-P part of this array must contain the
          input/state matrix BR of the system R.

  LDBR    INTEGER
          The leading dimension of array BR.  LDBR >= MAX(1,N).

  DR      (input/output) DOUBLE PRECISION array, dimension (LDDR,P)
          On entry, the leading P-by-P part of this array must
          contain the input/output matrix DR of the system R.
          On exit, the leading P-by-P part of this array contains
          the LU factorization of the matrix DR, as computed by
          LAPACK Library routine DGETRF.

  LDDR    INTEGER
          The leading dimension of array DR.  LDDR >= MAX(1,P).

  IWORK   INTEGER array, dimension (P)

  DWORK   DOUBLE PRECISION array, dimension (MAX(1,4*P))
          On exit, DWORK(1) contains an estimate of the reciprocal
          condition number of the matrix DR.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value;
          = 1:  the matrix DR is singular;
          = 2:  the matrix DR is numerically singular (warning);
                the calculations continued.

  The subroutine computes the matrices of the state-space
  representation G = (A,B,C,D) by using the formulas:

                   -1              -1
  A = AQR - BR * DR  * CQR,  C = DR  * CQR,
                   -1              -1
  B = BQ  - BR * DR  * DQ,   D = DR  * DQ.

  [1] Varga A.
      Coprime factors model reduction method based on
      square-root balancing-free techniques.
      System Analysis, Modelling and Simulation,
      vol. 11, pp. 303-311, 1993.

  None

Program Text

  None

  None

  None

Return to index