Fundamental Identification Limit of Single-Input and Single-Output Linear Time-Invariant Systems

This paper considers the identification problem of the system parameters of discrete-time linear time-invariant(LTI) systems. Based on a limited number of input/output sample trajectories, under the condition of the total energy of input is limited and input can fully excite the state of the system, we give the fundamental identification limit of system parameters (up to a similarity transformation) for marginally stable single-input and single-output(SISO) systems by using Cramer-Rao bound, and we show that the identification of system parameters become more and more difficult as the system dimension increases.