Determination of system-matrices of linear continuous-time multivariable systems from discrete-time models

It is shown that the computed system matrix for a continuous-time multivariable system may have the imaginary parts of its eigenvalues shifted from their true values when the matrix is determined from a discrete-time model. The same type of eigenvalue shift also can occur if a kth root of a matrix is used in the system identification. A numerical example is given to show that either predicted eigenvalue shift can occur. A bound on the sampling interval is suggested to avoid eigenvalue shifts.