Abstract
A new simple method of identification for linear discrete systems has been developed, which is based on Kalman's Hankel matrix H formed by Markov parameters of the system.
By input random sequences generated by a computer, input Hankel type matrix U is formed. Matrix Y which is the product of matrices U and H, that is Y=U×H, plays the crucial roles in this identification method, because useful properties are transferred from Matrix H.
The identification for system dimension can be implemented by upper left sub-matrixY'. If system dimension is n0, then Y' must be (2n0-1)by n0 matrix. After multiplying Y' by fundamental matrix chain Sn0-1, …, S2, S1 from the left, n0 by n0 matrix Y0 can be obtained, the rank of which is equal to the system dimension. Increasing n0 by one, the diagonalized matrix Y0' becomes singular, but the parameters of the denominator of the transfer function appear on the (n0+1)th column. So only n0 iterations are required to complete system identification.
