Convergence and convergence rate of the balanced realization truncations for infinite-dimensional discrete-time systems

In this paper, we study approximation via balanced realizations for a large class of infinite-dimensional discrete-time linear systems. We give properties of the truncated system and prove that the approximation is L₂-convergent. In the case of nuclear systems, we prove convergence in nuclear norm and give an estimation of the L_∞-convergence rate.