# findAC

discrete-time system subspace identification

### Syntax

```[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
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