Random Matrix-Based Approach for Uncertainty Analysis of the Eigensystem Realization Algorithm

In this paper, uncertainty in the state space matrices in a linear stochastic time-invariant discrete time system is presented by performing uncertainty analysis of the eigensystem realization algorithm (ERA). An analytical expression for the calculation of the singular values of Hankel matrix is developed. The expression for the joint distribution of the singular values is used to estimate the rank of the Hankel matrix. The distribution of singular values is also used to find the distribution on the bound of norm of system matrix.