tailieunhanh - Model reduction in schur basis with

We propose a new algorithm to obtain a reduced model with pole retention. The main idea is that instead of transforming A into diagonal matrix as in modal truncation technique, we transform A into upper-triangle matrix. The H∞-norm error bound of this algorithm is given. The choice of pole retention will be discussed to get reduced model having minimal H∞-norm error bound. | Đào Huy Du và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 139(09): 237 - 244 MODEL REDUCTION IN SCHUR BASIS WITH POLE RETENTION AND H∞-NORM ERROR BOUND Dao Huy Du1*, Ha Binh Minh2 1 College of Technology – TNU, Hanoi University of Science and Technology, VN 2 SUMMARY We propose a new algorithm to obtain a reduced model with pole retention. The main idea is that instead of transforming A into diagonal matrix as in modal truncation technique, we transform A into upper-triangle matrix. The H∞-norm error bound of this algorithm is given. The choice of pole retention will be discussed to get reduced model having minimal H∞-norm error bound. Key words: linear time-invariant systems, modal truncation, pole retention, H∞-norm error bound, triangle realization, triangle truncation. INTRODUCTION* Modal approximation is simple and effective technique in model reduction. This technique retains a part of the poles of original system. The reduced model therefore retains some physical interpretations of the original one, such as some vibration modes. Modal approximation technique also provides an error bound formula, which is useful to give the first estimation of how many state or pole need to be discasted. Modal approximation techniqueis based on selecting the poles which are important for model reduction’s purposes. There are two ways to select these poles. The first one can be classified as “top-down” methods, in which we search every poles and then select the important ones. Modal truncation method, which is discussed in Section 2, belongs to this class. The second one can be classified as “bottom-up” methods, in which we search pole one-by-one and then compare the new pole we found to the set of poles found before. If the new pole is better than others then we select, otherwise we discaste. Some numerical methods developed recently in [7,8] belong to this class. The aim of this paper is to improve modal truncation method. The idea of truncation’ can be divided into two steps: .