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


.. _findBDK: findBDK.html
.. _sident: sident.html
.. _findR: findR.html
.. _sorder: sorder.html
.. _findABCD: findABCD.html
.. _findBD: findBD.html