Before revision:  The approximation of the state-transition operators  determined primarily by matrices of parameters to be identified based on data measured from a given system, is approached by proving the existence of low-rank approximations of submatrices of the trajectory matrices corresponding to the measured data, that can be used to compute approximate sparse representations of the matrices of parameters.
After revision:  The approximation of the state-transition operators determined primarily by matrices of parameters to be identified based on data measured from a given system, is approached by identifying conditions for the existence of low-rank approximations of submatrices of the trajectory matrices corresponding to the measured data, that can be used to compute approximate sparse representations of the matrices of parameters.