## SB10JD

### Converting a descriptor state-space system into regular state-space form

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

Purpose

      To convert the descriptor state-space system

      E*dx/dt = A*x + B*u
            y = C*x + D*u

      into regular state-space form

       dx/dt = Ad*x + Bd*u
           y = Cd*x + Dd*u .

Specification

          SUBROUTINE SB10JD( N, M, NP, A, LDA, B, LDB, C, LDC, D, LDD, E,
         $                   LDE, NSYS, DWORK, LDWORK, INFO )
    C     .. Scalar Arguments ..
          INTEGER            INFO, LDA, LDB, LDC, LDD, LDE, LDWORK, M, N,
         $                   NP, NSYS
    C     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * ),
         $                   D( LDD, * ), DWORK( * ),  E( LDE, * )

Arguments

Input/Output Parameters

      N       (input) INTEGER
              The order of the descriptor 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.

      A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the leading N-by-N part of this array must
              contain the state matrix A of the descriptor system.
              On exit, the leading NSYS-by-NSYS part of this array
              contains the state matrix Ad of the converted system.

      LDA     INTEGER
              The leading dimension of the 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 matrix B of the descriptor system.
              On exit, the leading NSYS-by-M part of this array
              contains the input matrix Bd of the converted system.

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

      C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
              On entry, the leading NP-by-N part of this array must
              contain the output matrix C of the descriptor system.
              On exit, the leading NP-by-NSYS part of this array
              contains the output matrix Cd of the converted system.

      LDC     INTEGER
              The leading dimension of the array C.  LDC >= max(1,NP).

      D       (input/output) DOUBLE PRECISION array, dimension (LDD,M)
              On entry, the leading NP-by-M part of this array must
              contain the matrix D of the descriptor system.
              On exit, the leading NP-by-M part of this array contains
              the matrix Dd of the converted system.

      LDD     INTEGER
              The leading dimension of the array D.  LDD >= max(1,NP).

      E       (input/output) DOUBLE PRECISION array, dimension (LDE,N)
              On entry, the leading N-by-N part of this array must
              contain the matrix E of the descriptor system.
              On exit, this array contains no useful information.

      LDE     INTEGER
              The leading dimension of the array E.  LDE >= max(1,N).

      NSYS    (output) INTEGER
              The order of the converted state-space system.

Workspace

      DWORK   DOUBLE PRECISION array, dimension (LDWORK)
              On exit, if INFO = 0, DWORK(1) contains the optimal value
              of LDWORK.

      LDWORK  INTEGER
              The dimension of the array DWORK.
              LDWORK >= max( 1, 2*N*N + 2*N + N*MAX( 5, N + M + NP ) ).
              For good performance, LDWORK must generally be larger.

Error Indicator

      INFO    INTEGER
              = 0:  successful exit;
              < 0:  if INFO = -i, the i-th argument had an illegal
                    value;
              = 1:  the iteration for computing singular value
                    decomposition did not converge.

Method

      The routine performs the transformations described in [1].

References

      [1] Chiang, R.Y. and Safonov, M.G.
          Robust Control Toolbox User's Guide.
          The MathWorks Inc., Natick, Mass., 1992.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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