## AB05QD

### Appending two systems in state-space form

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

Purpose

      To append two systems G1 and G2 in state-space form together.
      If G1 = (A1,B1,C1,D1) and G2 = (A2,B2,C2,D2) are the state-space
      models of the given two systems having the transfer-function
      matrices G1 and G2, respectively, this subroutine constructs the
      state-space model G = (A,B,C,D) which corresponds to the
      transfer-function matrix

                            ( G1 0  )
                        G = (       )
                            ( 0  G2 )

Specification

          SUBROUTINE AB05QD( OVER, N1, M1, P1, N2, M2, P2, A1, LDA1, B1,
         $                   LDB1, C1, LDC1, D1, LDD1, A2, LDA2, B2, LDB2,
         $                   C2, LDC2, D2, LDD2, N, M, P, A, LDA, B, LDB,
         $                   C, LDC, D, LDD, INFO )
    C     .. Scalar Arguments ..
          CHARACTER         OVER
          INTEGER           INFO, LDA, LDA1, LDA2, LDB, LDB1, LDB2, LDC,
         $                  LDC1, LDC2, LDD, LDD1, LDD2, M, M1, M2, N, N1,
         $                  N2, P, P1, P2
    C     .. Array Arguments ..
          DOUBLE PRECISION  A(LDA,*), A1(LDA1,*), A2(LDA2,*), B(LDB,*),
         $                  B1(LDB1,*), B2(LDB2,*), C(LDC,*), C1(LDC1,*),
         $                  C2(LDC2,*), D(LDD,*), D1(LDD1,*), D2(LDD2,*)

Arguments

Mode Parameters

      OVER    CHARACTER*1
              Indicates whether the user wishes to overlap pairs of
              arrays, as follows:
              = 'N':  Do not overlap;
              = 'O':  Overlap pairs of arrays: A1 and A, B1 and B,
                      C1 and C, and D1 and D, i.e. the same name is
                      effectively used for each pair (for all pairs)
                      in the routine call.  In this case, setting
                      LDA1 = LDA, LDB1 = LDB, LDC1 = LDC, and LDD1 = LDD
                      will give maximum efficiency.

Input/Output Parameters

      N1      (input) INTEGER
              The number of state variables in the first system, i.e.
              the order of the matrix A1, the number of rows of B1 and
              the number of columns of C1.  N1 >= 0.

      M1      (input) INTEGER
              The number of input variables in the first system, i.e.
              the number of columns of matrices B1 and D1.  M1 >= 0.

      P1      (input) INTEGER
              The number of output variables in the first system, i.e.
              the number of rows of matrices C1 and D1.  P1 >= 0.

      N2      (input) INTEGER
              The number of state variables in the second system, i.e.
              the order of the matrix A2, the number of rows of B2 and
              the number of columns of C2.  N2 >= 0.

      M2      (input) INTEGER
              The number of input variables in the second system, i.e.
              the number of columns of matrices B2 and D2.  M2 >= 0.

      P2      (input) INTEGER
              The number of output variables in the second system, i.e.
              the number of rows of matrices C2 and D2.  P2 >= 0.

      A1      (input) DOUBLE PRECISION array, dimension (LDA1,N1)
              The leading N1-by-N1 part of this array must contain the
              state transition matrix A1 for the first system.

      LDA1    INTEGER
              The leading dimension of array A1.  LDA1 >= MAX(1,N1).

      B1      (input) DOUBLE PRECISION array, dimension (LDB1,M1)
              The leading N1-by-M1 part of this array must contain the
              input/state matrix B1 for the first system.

      LDB1    INTEGER
              The leading dimension of array B1.  LDB1 >= MAX(1,N1).

      C1      (input) DOUBLE PRECISION array, dimension (LDC1,N1)
              The leading P1-by-N1 part of this array must contain the
              state/output matrix C1 for the first system.

      LDC1    INTEGER
              The leading dimension of array C1.
              LDC1 >= MAX(1,P1) if N1 > 0.
              LDC1 >= 1 if N1 = 0.

      D1      (input) DOUBLE PRECISION array, dimension (LDD1,M1)
              The leading P1-by-M1 part of this array must contain the
              input/output matrix D1 for the first system.

      LDD1    INTEGER
              The leading dimension of array D1.  LDD1 >= MAX(1,P1).

      A2      (input) DOUBLE PRECISION array, dimension (LDA2,N2)
              The leading N2-by-N2 part of this array must contain the
              state transition matrix A2 for the second system.

      LDA2    INTEGER
              The leading dimension of array A2.  LDA2 >= MAX(1,N2).

      B2      (input) DOUBLE PRECISION array, dimension (LDB2,M2)
              The leading N2-by-M2 part of this array must contain the
              input/state matrix B2 for the second system.

      LDB2    INTEGER
              The leading dimension of array B2.  LDB2 >= MAX(1,N2).

      C2      (input) DOUBLE PRECISION array, dimension (LDC2,N2)
              The leading P2-by-N2 part of this array must contain the
              state/output matrix C2 for the second system.

      LDC2    INTEGER
              The leading dimension of array C2.
              LDC2 >= MAX(1,P2) if N2 > 0.
              LDC2 >= 1 if N2 = 0.

      D2      (input) DOUBLE PRECISION array, dimension (LDD2,M2)
              The leading P2-by-M2 part of this array must contain the
              input/output matrix D2 for the second system.

      LDD2    INTEGER
              The leading dimension of array D2.  LDD2 >= MAX(1,P2).

      N       (output) INTEGER
              The number of state variables (N1 + N2) in the resulting
              system, i.e. the order of the matrix A, the number of rows
              of B and the number of columns of C.

      M       (output) INTEGER
              The number of input variables (M1 + M2) in the resulting
              system, i.e. the number of columns of B and D.

      P       (output) INTEGER
              The number of output variables (P1 + P2) of the resulting
              system, i.e. the number of rows of C and D.

      A       (output) DOUBLE PRECISION array, dimension (LDA,N1+N2)
              The leading N-by-N part of this array contains the state
              transition matrix A for the resulting system.
              The array A can overlap A1 if OVER = 'O'.

      LDA     INTEGER
              The leading dimension of array A.  LDA >= MAX(1,N1+N2).

      B       (output) DOUBLE PRECISION array, dimension (LDB,M1+M2)
              The leading N-by-M part of this array contains the
              input/state matrix B for the resulting system.
              The array B can overlap B1 if OVER = 'O'.

      LDB     INTEGER
              The leading dimension of array B.  LDB >= MAX(1,N1+N2).

      C       (output) DOUBLE PRECISION array, dimension (LDC,N1+N2)
              The leading P-by-N part of this array contains the
              state/output matrix C for the resulting system.
              The array C can overlap C1 if OVER = 'O'.

      LDC     INTEGER
              The leading dimension of array C.
              LDC >= MAX(1,P1+P2) if N1+N2 > 0.
              LDC >= 1 if N1+N2 = 0.

      D       (output) DOUBLE PRECISION array, dimension (LDD,M1+M2)
              The leading P-by-M part of this array contains the
              input/output matrix D for the resulting system.
              The array D can overlap D1 if OVER = 'O'.

      LDD     INTEGER
              The leading dimension of array D.  LDD >= MAX(1,P1+P2).

Error Indicator

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

Method

      The matrices of the resulting systems are determined as:

            ( A1   0  )         ( B1  0  )
        A = (         ) ,   B = (        ) ,
            ( 0    A2 )         ( 0   B2 )

            ( C1   0  )         ( D1  0  )
        C = (         ) ,   D = (        ) .
            ( 0    C2 )         ( 0   D2 )

References

      None

Further Comments

      None

Example

Program Text

    *     AB05QD EXAMPLE PROGRAM TEXT
    *
    *     .. Parameters ..
          INTEGER          NIN, NOUT
          PARAMETER        ( NIN = 5, NOUT = 6 )
          INTEGER          N1MAX, N2MAX, NMAX, M1MAX, M2MAX, MMAX, P1MAX,
         $                 P2MAX, PMAX
          PARAMETER        ( N1MAX = 20, N2MAX = 20, NMAX = N1MAX+N2MAX,
         $                   M1MAX = 20, M2MAX = 20, MMAX = M1MAX+M2MAX,
         $                   P1MAX = 20, P2MAX = 20, PMAX = P1MAX+P2MAX )
          INTEGER          LDA, LDA1, LDA2, LDB, LDB1, LDB2, LDC, LDC1,
         $                 LDC2, LDD, LDD1, LDD2
          PARAMETER        ( LDA = NMAX, LDA1 = N1MAX, LDA2 = N2MAX,
         $                   LDB = NMAX, LDB1 = N1MAX, LDB2 = N2MAX,
         $                   LDC = PMAX, LDC1 = P1MAX, LDC2 = P1MAX,
         $                   LDD = PMAX, LDD1 = P1MAX, LDD2 = P1MAX )
          DOUBLE PRECISION ONE
          PARAMETER        ( ONE=1.0D0 )
    *     .. Local Scalars ..
          CHARACTER*1      OVER
          INTEGER          I, INFO, J, M, M1, M2, N, N1, N2, P, P1, P2
    *     .. Local Arrays ..
          DOUBLE PRECISION A(LDA,NMAX), A1(LDA1,N1MAX), A2(LDA2,N2MAX),
         $                 B(LDB,MMAX), B1(LDB1,M1MAX), B2(LDB2,M2MAX),
         $                 C(LDC,NMAX), C1(LDC1,N1MAX), C2(LDC2,N2MAX),
         $                 D(LDD,MMAX), D1(LDD1,M1MAX), D2(LDD2,M2MAX)
    *     .. External Subroutines ..
          EXTERNAL         AB05QD
    *     .. Executable Statements ..
    *
          OVER = 'N'
          WRITE ( NOUT, FMT = 99999 )
    *     Skip the heading in the data file and read the data.
          READ ( NIN, FMT = '()' )
          READ ( NIN, FMT = * ) N1, M1, P1, N2, M2, P2
          IF ( N1.LE.0 .OR. N1.GT.N1MAX ) THEN
             WRITE ( NOUT, FMT = 99992 ) N1
          ELSE
             READ ( NIN, FMT = * ) ( ( A1(I,J), J = 1,N1 ), I = 1,N1 )
             IF ( M1.LE.0 .OR. M1.GT.M1MAX ) THEN
                WRITE ( NOUT, FMT = 99991 ) M1
             ELSE
                READ ( NIN, FMT = * ) ( ( B1(I,J), I = 1,N1 ), J = 1,M1 )
                IF ( P1.LE.0 .OR. P1.GT.P1MAX ) THEN
                   WRITE ( NOUT, FMT = 99990 ) P1
                ELSE
                   READ ( NIN, FMT = * ) ( ( C1(I,J), J = 1,N1 ), I = 1,P1 )
                   READ ( NIN, FMT = * ) ( ( D1(I,J), J = 1,M1 ), I = 1,P1 )
                   IF ( N2.LE.0 .OR. N2.GT.N2MAX ) THEN
                      WRITE ( NOUT, FMT = 99989 ) N2
                   ELSE
                      READ ( NIN, FMT = * )
         $                 ( ( A2(I,J), J = 1,N2 ), I = 1,N2 )
                      IF ( M2.LE.0 .OR. M2.GT.M2MAX ) THEN
                         WRITE ( NOUT, FMT = 99988 ) M2
                      ELSE
                         READ ( NIN, FMT = * )
         $                    ( ( B2(I,J), I = 1,N2 ), J = 1,M2 )
                         IF ( P2.LE.0 .OR. P2.GT.P2MAX ) THEN
                            WRITE ( NOUT, FMT = 99987 ) P2
                         ELSE
                            READ ( NIN, FMT = * )
         $                       ( ( C2(I,J), J = 1,N2 ), I = 1,P2 )
                            READ ( NIN, FMT = * )
         $                       ( ( D2(I,J), J = 1,M2 ), I = 1,P2 )
    *                          Find the state-space model (A,B,C,D).
                            CALL AB05QD( OVER, N1, M1, P1, N2, M2, P2, A1,
         $                               LDA1, B1, LDB1, C1, LDC1, D1, LDD1,
         $                               A2, LDA2, B2, LDB2, C2, LDC2, D2,
         $                               LDD2, N, M, P, A, LDA, B, LDB, C,
         $                               LDC, D, LDD, INFO )
    *
                            IF ( INFO.NE.0 ) THEN
                               WRITE ( NOUT, FMT = 99998 ) INFO
                            ELSE
                               WRITE ( NOUT, FMT = 99997 )
                               DO 20 I = 1, N
                                  WRITE ( NOUT, FMT = 99996 )
         $                              ( A(I,J), J = 1,N )
       20                      CONTINUE
                               WRITE ( NOUT, FMT = 99995 )
                               DO 40 I = 1, N
                                  WRITE ( NOUT, FMT = 99996 )
         $                              ( B(I,J), J = 1,M )
       40                      CONTINUE
                               WRITE ( NOUT, FMT = 99994 )
                               DO 60 I = 1, P
                                  WRITE ( NOUT, FMT = 99996 )
         $                              ( C(I,J), J = 1,N )
       60                      CONTINUE
                               WRITE ( NOUT, FMT = 99993 )
                               DO 80 I = 1, P
                                  WRITE ( NOUT, FMT = 99996 )
         $                              ( D(I,J), J = 1,M )
       80                      CONTINUE
                            END IF
                         END IF
                      END IF
                   END IF
                END IF
             END IF
          END IF
          STOP
    *
    99999 FORMAT (' AB05QD EXAMPLE PROGRAM RESULTS',/1X)
    99998 FORMAT (' INFO on exit from AB05QD = ',I2)
    99997 FORMAT (' The state transition matrix of the connected system is')
    99996 FORMAT (20(1X,F8.4))
    99995 FORMAT (/' The input/state matrix of the connected system is ')
    99994 FORMAT (/' The state/output matrix of the connected system is ')
    99993 FORMAT (/' The input/output matrix of the connected system is ')
    99992 FORMAT (/' N1 is out of range.',/' N1 = ',I5)
    99991 FORMAT (/' M1 is out of range.',/' M1 = ',I5)
    99990 FORMAT (/' P1 is out of range.',/' P1 = ',I5)
    99989 FORMAT (/' N2 is out of range.',/' N2 = ',I5)
    99988 FORMAT (/' M2 is out of range.',/' M2 = ',I5)
    99987 FORMAT (/' P2 is out of range.',/' P2 = ',I5)
          END

Program Data

     AB05QD EXAMPLE PROGRAM DATA
       3     2     2     3     2     2
       1.0   0.0  -1.0
       0.0  -1.0   1.0
       1.0   1.0   2.0
       1.0   1.0   0.0
       2.0   0.0   1.0
       3.0  -2.0   1.0
       0.0   1.0   0.0
       1.0   0.0
       0.0   1.0
      -3.0   0.0   0.0
       1.0   0.0   1.0
       0.0  -1.0   2.0
       0.0  -1.0   0.0
       1.0   0.0   2.0
       1.0   1.0   0.0
       1.0   1.0  -1.0
       1.0   1.0
       0.0   1.0

Program Results

     AB05QD EXAMPLE PROGRAM RESULTS

     The state transition matrix of the connected system is
       1.0000   0.0000  -1.0000   0.0000   0.0000   0.0000
       0.0000  -1.0000   1.0000   0.0000   0.0000   0.0000
       1.0000   1.0000   2.0000   0.0000   0.0000   0.0000
       0.0000   0.0000   0.0000  -3.0000   0.0000   0.0000
       0.0000   0.0000   0.0000   1.0000   0.0000   1.0000
       0.0000   0.0000   0.0000   0.0000  -1.0000   2.0000

     The input/state matrix of the connected system is
       1.0000   2.0000   0.0000   0.0000
       1.0000   0.0000   0.0000   0.0000
       0.0000   1.0000   0.0000   0.0000
       0.0000   0.0000   0.0000   1.0000
       0.0000   0.0000  -1.0000   0.0000
       0.0000   0.0000   0.0000   2.0000

     The state/output matrix of the connected system is
       3.0000  -2.0000   1.0000   0.0000   0.0000   0.0000
       0.0000   1.0000   0.0000   0.0000   0.0000   0.0000
       0.0000   0.0000   0.0000   1.0000   1.0000   0.0000
       0.0000   0.0000   0.0000   1.0000   1.0000  -1.0000

     The input/output matrix of the connected system is
       1.0000   0.0000   0.0000   0.0000
       0.0000   1.0000   0.0000   0.0000
       0.0000   0.0000   1.0000   1.0000
       0.0000   0.0000   0.0000   1.0000

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