findAC

discrete-time system subspace identification

Calling Sequence

[A,C] = findAC(S,N,L,R,METH,TOL,PRINTW)
[A,C,RCND] = findAC(S,N,L,R,METH,TOL,PRINTW)

Arguments

:S integer, the number of block rows in the block-Hankel matrices : :N integer : :L integer : :R matrix, relevant part of the R factor of the concatenated block-

Hankel matrices computed by a call to findr.

: :METH integer, an option for the method to use

:= 1 MOESP method with past inputs and outputs; : := 2 N4SID method; :

Default: METH = 3. : :TOL the tolerance used for estimating the rank of matrices. If TOL

> 0, then the given value of TOL is used as a lower bound for the reciprocal condition number. Default: prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.

: :PRINTW integer, switch for printing the warning messages.

PRINTW = 1:print warning messages;

: := 0 do not print warning messages. :

Default: PRINTW = 0. : :A matrix, state system matrix : :C matrix, output system matrix : :RCND vector of length 4, condition numbers of the matrices involved

in rank decision

:

Description

finds the system matrices A and C of a discrete-time system, given the system order and the relevant part of the R factor of the concatenated block-Hankel matrices, using subspace identification techniques (MOESP or N4SID).

• [A,C] = findAC(S,N,L,R,METH,TOL,PRINTW) computes the system matrices A and C. The model structure is: x(k+1) = Ax(k) + Bu(k) + Ke(k), k >= 1, y(k) = Cx(k) + Du(k) + e(k), where x(k) and y(k) are vectors of length N and L, respectively.
• [A,C,RCND] = findAC(S,N,L,R,METH,TOL,PRINTW) also returns the vector RCND of length 4 containing the condition numbers of the matrices involved in rank decisions.

Matrix R, computed by findR, should be determined with suitable arguments METH and JOBD.

Examples

//generate data from a given linear system
A = [ 0.5, 0.1,-0.1, 0.2;
      0.1, 0,  -0.1,-0.1;
     -0.4,-0.6,-0.7,-0.1;
      0.8, 0,  -0.6,-0.6];
B = [0.8;0.1;1;-1];
C = [1 2 -1 0];
SYS=`syslin`_(0.1,A,B,C);
nsmp=100;
U=`prbs_a`_(nsmp,nsmp/5);
Y=(`flts`_(U,SYS)+0.3*`rand`_(1,nsmp,'normal'));

// Compute R
S=15;L=1;
[R,N,SVAL] = `findR`_(S,Y',U');

N=3;
METH=3;TOL=-1;
[A,C] = findAC(S,N,L,R,METH,TOL);

See Also

• findABCD discrete-time system subspace identification
• findBD initial state and system matrices B and D of a discrete- time system
• findBDK Kalman gain and B D system matrices of a discrete-time system
• findR Preprocessor for estimating the matrices of a linear time- invariant dynamical system
• sorder computing the order of a discrete-time system
• sident discrete-time state-space realization and Kalman gain