On model reduction using LMI´s

We deal with the problem of approximating a given n-th order LTI system G by an r-th order system Gr where r < n. It is shown that lower bounds of the H/sub /spl infin// norm of the associated error system can be analyzed by using LMI-related techniques. These lower bounds are given in terms of the Hankel singular values of the system G and coincide with those obtained in the previous studies where the analysis of the Hankel operators plays a central role. Thus, this paper provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMI´s. Moreover, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the problem is essentially convex and the optimal reduced-order models can be constructed via LMI optimization.