findR - Preprocessor for estimating the matrices of a linear time-invariant dynamical system
Default: METH = 1.
Default: ALG = 1.
Default: JOBD = 2. This parameter is not relevant for METH = 2.
Default: TOL(1) = prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.
When TOL(2) = 0, then S*epsilon_machine*sval(1) is used instead TOL(2), where sval(1) is the maximal singular value. When TOL(2) < 0, the estimate is indicated by the index of the singular value that has the largest logarithmic gap to its successor. Default: TOL(2) = -1.
Default: PRINTW = 0.
findR Preprocesses the input-output data for estimating the matrices of a linear time-invariant dynamical system, using Cholesky or (fast) QR factorization and subspace identification techniques (MOESP or N4SID), and estimates the system order.
[R,N] = findR(S,Y,U,METH,ALG,JOBD,TOL,PRINTW) returns the processed upper triangular factor R of the concatenated block-Hankel matrices built from the input-output data, and the order N of a discrete-time realization. The model structure is:
x(k+1) = Ax(k) + Bu(k) + w(k), k >= 1, y(k) = Cx(k) + Du(k) + e(k).
The vectors y(k) and u(k) are transposes of the k-th rows of Y and U, respectively.
[R,N,SVAL,RCND] = findR(S,Y,U,METH,ALG,JOBD,TOL,PRINTW) also returns the singular values SVAL, used for estimating the order, as well as, if meth = 2, the vector RCND of length 2 containing the reciprocal condition numbers of the matrices involved in rank decisions or least squares solutions.
[R,N] = findR(S,Y) assumes U =  and default values for the remaining input arguments.
//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); U=(ones(1,1000)+rand(1,1000,'normal')); Y=(flts(U,SYS)+0.5*rand(1,1000,'normal')); // Compute R [R,N,SVAL] = findR(15,Y',U'); SVAL N