TB01VY

Conversion of the output normal form to a state-space representation

Purpose

  To convert the linear discrete-time system given as its output
  normal form [1], with parameter vector THETA, into the state-space
  representation (A, B, C, D), with the initial state x0.

      SUBROUTINE TB01VY( APPLY, N, M, L, THETA, LTHETA, A, LDA, B, LDB,
     $                   C, LDC, D, LDD, X0, DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         APPLY
      INTEGER           INFO, L, LDA, LDB, LDC, LDD, LDWORK, LTHETA, M,
     $                  N
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*),
     $                  DWORK(*), THETA(*), X0(*)

Mode Parameters

  APPLY   CHARACTER*1
          Specifies whether or not the parameter vector should be
          transformed using a bijective mapping, as follows:
          = 'A' : apply the bijective mapping to the N vectors in
                  THETA corresponding to the matrices A and C;
          = 'N' : do not apply the bijective mapping.
          The transformation performed when APPLY = 'A' allows
          to get rid of the constraints norm(THETAi) < 1, i = 1:N.
          A call of the SLICOT Library routine TB01VD associated to
          a call of TB01VY must use the same value of APPLY.

  N       (input) INTEGER
          The order of the system.  N >= 0.

  M       (input) INTEGER
          The number of system inputs.  M >= 0.

  L       (input) INTEGER
          The number of system outputs.  L >= 0.

  THETA   (input) DOUBLE PRECISION array, dimension (LTHETA)
          The leading N*(L+M+1)+L*M part of this array must contain
          the parameter vector that defines a system (A, B, C, D),
          with the initial state x0. The parameters are:

          THETA(1:N*L)                      : parameters for A, C;
          THETA(N*L+1:N*(L+M))              : parameters for B;
          THETA(N*(L+M)+1:N*(L+M)+L*M)      : parameters for D;
          THETA(N*(L+M)+L*M+1:N*(L+M+1)+L*M): parameters for x0.

  LTHETA  INTEGER
          The length of array THETA.  LTHETA >= N*(L+M+1)+L*M.

  A       (output) DOUBLE PRECISION array, dimension (LDA,N)
          The leading N-by-N part of this array contains the system
          state matrix corresponding to the output normal form with
          parameter vector THETA.

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

  B       (output) DOUBLE PRECISION array, dimension (LDB,M)
          The leading N-by-M part of this array contains the system
          input matrix corresponding to the output normal form with
          parameter vector THETA.

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

  C       (output) DOUBLE PRECISION array, dimension (LDC,N)
          The leading L-by-N part of this array contains the system
          output matrix corresponding to the output normal form with
          parameter vector THETA.

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

  D       (output) DOUBLE PRECISION array, dimension (LDD,M)
          The leading L-by-M part of this array contains the system
          input/output matrix corresponding to the output normal
          form with parameter vector THETA.

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

  X0      (output) DOUBLE PRECISION array, dimension (N)
          This array contains the initial state of the system, x0,
          corresponding to the output normal form with parameter
          vector THETA.

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)

  LDWORK  INTEGER
          The length of the array DWORK.
          LDWORK >= N*(N+L+1).

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

  The parameters characterizing A and C are used to build N
  orthogonal transformations, which are then applied to recover
  these matrices.

  None

Program Text

  None

  None

  None