Scilab Function

findABCD - discrete-time system subspace identification

Calling Sequence




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.

    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.


    See Also