Model Reduction for Linear Time-Invariant Discrete-Time Systems Using Matrix Inequalities

摘要

In this paper, we deal with the H{sub}∞ model reduction problems for discrete-time systems. It is shown that a lower bound of the H{sub}∞, norm of the error systems can be obtained by using the well-established LMI-related techniques. Moreover, when we reduce the order by the multiplicity of the smallest Hankel singular value of the system to be reduced, we show that the lower bound is indeed the infimum and the optimal reduced-order model that attains this infimum can be constructured via LMI optimization.