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.
Specification
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,*)
Arguments
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).
Workspace
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.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Method
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.
References
[1] Luenberger, D.G.
Introduction to Dynamic Systems: Theory, Models and
Applications.
John Wiley & Sons, New York, 1979.
Numerical Aspects
The algorithm requires approximately (N + M) x (N + P) x NY multiplications and additions.Further Comments
The implementation exploits data locality as much as possible, given the workspace length.Example
Program Text
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