findR Preprocessor for estimating the matrices of a linear time-invariant dynamical system [R,N [,SVAL,RCND]] = findR(S,Y,U,METH,ALG,JOBD,TOL,PRINTW) [R,N] = findR(S,Y) S the number of block rows in the block-Hankel matrices. Y U METH an option for the method to use: 1 MOESP method with past inputs and outputs; 2 N4SI15 0 1 1 1000D method. Default: METH = 1. ALG an option for the algorithm to compute the triangular factor of the concatenated block-Hankel matrices built from the input-output data: 1 Cholesky algorithm on the correlation matrix; 2 fast QR algorithm; 3 standard QR algorithm. Default: ALG = 1. JOBD an option to specify if the matrices B and D should later be computed using the MOESP approach: = 1 : the matrices B and D should later be computed using the MOESP approach; = 2 : the matrices B and D should not be computed using the MOESP approach. Default: JOBD = 2. This parameter is not relevant for METH = 2. TOL a vector of length 2 containing tolerances: TOL (1) is the tolerance for estimating the rank of matrices. If TOL(1) > 0, the given value of TOL(1) is used as a lower bound for the reciprocal condition number. Default: TOL(1) = prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision. TOL (2) is the tolerance for estimating the system order. If TOL(2) >= 0, the estimate is indicated by the index of the last singular value greater than or equal to TOL(2). (Singular values less than TOL(2) are considered as zero.) 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. PRINTW a switch for printing the warning messages. = 1: print warning messages; = 0: do not print warning messages. Default: PRINTW = 0. R N the order of the discrete-time realization SVAL singular values SVAL, used for estimating the order. RCND vector of length 2 containing the reciprocal condition numbers of the matrices involved in rank decisions or least squares solutions. 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: = 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. findABCD findAC findBD findBDK sorder sident