TF01MX

Output sequence of a linear time-invariant open-loop system given its system matrix

Purpose

  To compute the output sequence of a linear time-invariant
  open-loop system given by its discrete-time state-space model
  with an (N+P)-by-(N+M) general system matrix S,

         ( A  B )
     S = (      ) .
         ( C  D )

  The initial state vector x(1) must be supplied by the user.

  The input and output trajectories are stored as in the SLICOT
  Library routine TF01MY.

      SUBROUTINE TF01MX( N, M, P, NY, S, LDS, U, LDU, X, Y, LDY,
     $                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, LDS, LDU, LDWORK, LDY, M, N, NY, P
C     .. Array Arguments ..
      DOUBLE PRECISION  DWORK(*), S(LDS,*), U(LDU,*), X(*), Y(LDY,*)

Input/Output Parameters

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

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

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

  NY      (input) INTEGER
          The number of output vectors y(k) to be computed.
          NY >= 0.

  S       (input) DOUBLE PRECISION array, dimension (LDS,N+M)
          The leading (N+P)-by-(N+M) part of this array must contain
          the system matrix S.

  LDS     INTEGER
          The leading dimension of array S.  LDS >= MAX(1,N+P).

  U       (input) DOUBLE PRECISION array, dimension (LDU,M)
          The leading NY-by-M part of this array must contain the
          input vector sequence u(k), for k = 1,2,...,NY.
          Specifically, the k-th row of U must contain u(k)'.

  LDU     INTEGER
          The leading dimension of array U.  LDU >= MAX(1,NY).

  X       (input/output) DOUBLE PRECISION array, dimension (N)
          On entry, this array must contain the initial state vector
          x(1) which consists of the N initial states of the system.
          On exit, this array contains the final state vector
          x(NY+1) of the N states of the system at instant NY+1.

  Y       (output) DOUBLE PRECISION array, dimension (LDY,P)
          The leading NY-by-P part of this array contains the output
          vector sequence y(1),y(2),...,y(NY) such that the k-th
          row of Y contains y(k)' (the outputs at instant k),
          for k = 1,2,...,NY.

  LDY     INTEGER
          The leading dimension of array Y.  LDY >= MAX(1,NY).

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)

  LDWORK  INTEGER
          The length of the array DWORK.
          LDWORK >= 0,        if MIN(N,P,NY) = 0;  otherwise,
          LDWORK >= N+P,      if M = 0;
          LDWORK >= 2*N+M+P,  if M > 0.
          For better performance, LDWORK should be larger.

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

  Given an initial state vector x(1), the output vector sequence
  y(1), y(2),..., y(NY) is obtained via the formulae

     ( x(k+1) )     ( x(k) )
     (        ) = S (      ) ,
     (  y(k)  )     ( u(k) )

  where each element y(k) is a vector of length P containing the
  outputs at instant k, and k = 1,2,...,NY.

  [1] Luenberger, D.G.
      Introduction to Dynamic Systems: Theory, Models and
      Applications.
      John Wiley & Sons, New York, 1979.

  The algorithm requires approximately (N + M) x (N + P) x NY
  multiplications and additions.

  The implementation exploits data locality as much as possible,
  given the workspace length.

Program Text

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