Error Norm Reduction in Structually Balanced Truncation

Abstract

In this paper, we attempt reducing an error norm in structurally balanced truncation. Structurally balanced truncation is a controller reduction method developed from balanced truncation (a model reduction method) and is carried out by solving Linear Matrix Inequalities (LMIs). In this method, it is easy to get an a priori error bound which depends on LMI solutions, however, it is difficult to obtain optimal LMI solutions because the optimaization problem has the objective function which is not convex. To overcome the difficulty, a suboptimal procedure is proposed by Zhou et al., however, their procedure can not decrease the a priori error bound sufficiently. So we propose an error norm reduction algorithm utilizing a linearized objective function (a linearized equation of a non-convex function associated with the error bound) and balancing matrices. Finally, the validity of the proposed method are verified by using numerical examples.