findABCDdiscrete-time system subspace identificationCalling Sequence[SYS,K] = findABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW)
SYS = findABCD(S,N,L,R,METH)
[SYS,K,Q,Ry,S,RCND] = findABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW)
[SYS,RCND] = findABCD(S,N,L,R,METH)
ArgumentsSinteger, the number of block rows in the block-Hankel matricesNinteger, the system orderLinteger, the number of outputRmatrix, relevant part of the R factor of the concatenated block-Hankel matrices computed by a call to findr.METHinteger, an option for the method to use= 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.
NSMPLinteger, 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.TOLthe 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.PRINTWinteger, switch for printing the warning messages.PRINTW= 1: print warning messages;PRINTW= 0: do not print warning messages.
Default: PRINTW = 0.
SYScomputes a state-space realization SYS = (A,B,C,D) (an syslin object)Kthe Kalman predictor gain K (if NSMPL > 0)Q state covarianceRyoutput covarianceSstate-output cross-covarianceRCNDvector, reciprocal condition numbers of the matrices involved in rank decisions, least squares or Riccati equation solutionsDescription
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:= 1,
y(k) = Cx(k) + Du(k) + e(k),
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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
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.
ExamplesSee Also
findAC
findBD
findBDK
findR
sorder
sident