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function [sys,K,Q,Ry,S,rcnd]=findABCD(s,n,l,R,meth,nsmpl,tol,printw)
sys=[];K=[];Q=[];Ry=[];S=[];rcnd=[];
[nargout,nargin] = argn(0)
//FINDABCD Finds the system matrices and the Kalman gain 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 and/or N4SID).
//
// [SYS,K] = FINDABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW) computes a state-
// space realization SYS = (A,B,C,D) (an ss object), and the Kalman
// predictor gain K (if NSMPL > 0). 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.
//
// [SYS,K,Q,Ry,S,RCND] = FINDABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW) also
// returns the state, output, and state-output (cross-)covariance
// matrices Q, Ry, and S (used for computing the Kalman gain), as well as
// the vector RCND of length lr containing the reciprocal condition numbers
// of the matrices involved in rank decisions, least squares or Riccati
// equation solutions, where
// lr = 4, if Kalman gain matrix K is not required, and
// lr = 12, if Kalman gain matrix K is required.
//
// S is the number of block rows in the block-Hankel matrices.
//
// METH is an option for the method to use:
// METH = 1 : MOESP method with past inputs and outputs;
// = 2 : N4SID method;
// = 3 : combined method: A and C via MOESP, B and D via N4SID.
// Default: METH = 3.
// Matrix R, computed by FINDR, should be determined with suitable arguments
// METH and JOBD. METH = 1 and JOBD = 1 must be used in findR, for METH = 1
// in FINDABCD; METH = 1 must be used in FINDR, for METH = 3 in FINDABCD.
//
// NSMPL is the total number of samples used for calculating the covariance
// matrices and the Kalman predictor gain. This parameter is not needed if
// the covariance matrices and/or the Kalman predictor gain matrix are not
// desired. If NSMPL = 0, then K, Q, Ry, and S are not computed.
// Default: NSMPL = 0.
//
// TOL is 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 is a select for printing the warning messages.
// PRINTW = 1: print warning messages;
// = 0: do not print warning messages.
// Default: PRINTW = 0.
//
// The number of output arguments may vary, but should correspond to the
// input arguments, e.g.,
// SYS = FINDABCD(S,N,L,R,METH) or
// [SYS,RCND] = FINDABCD(S,N,L,R,METH) just return SYS, or SYS and RCND.
//
// See also FINDAC, FINDBD, FINDBDK, FINDR, ORDER, SIDENT
//
// V. Sima 18-01-2000.
//
// Revisions:
//
nin = nargin;
nout = nargout;
//
if nin<8 then
printw = 0;
end
if nin<7 then tol = 0;end
if tol==[] then tol = 0;end
if nin<6 then nsmpl = 0;end
if nsmpl==[] then nsmpl = 0;end
if nin<5 then meth = 3;end
if meth==[] then meth = 3;end
if nin<4 then
error('Wrong number of input arguments');
end
//
// Compute all system matrices.
job = 1;
if nout==1 then
[A,C,B,D] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
elseif nout>=2 then
if nsmpl==0 then
// Here K means rcnd.
[A,C,B,D,K] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
elseif nout==2 then
[A,C,B,D,K] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
elseif nout==3 then
[A,C,B,D,K,Q] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
elseif nout==4 then
[A,C,B,D,K,Q,Ry] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
elseif nout==5 then
[A,C,B,D,K,Q,Ry,S] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
elseif nout==6 then
[A,C,B,D,K,Q,Ry,S,rcnd] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw);
else
error('Wrong number of output arguments');
end
else
error('Wrong number of output arguments');
end
//
sys = syslin(1,A,B,C,D);
//
// end findABCD
endfunction
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