H∞-based model order reduction using LMIs

In this paper new sufficient conditions are presented for the existence of a Lyapunov pair with a coupling rank constraint within a H∞ minimization framework derived using the bounded real lemma and the projection lemma. The conditions are then used to propose a Linear Matrix Inequality (LMI) sub-optimal method to solve the model order reduction problem of general non-square LTI systems with a prescribed number of states to be removed. This alleviates the need for trace or rank minimization, iterations, or a priori choice of any new additional variable. The effectiveness and stability of the proposed LMI method is demonstrated by applications to several model order reduction problems.