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# 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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