Linear Matrix Inequalities Application for Model Order Reduction with Rank Constraint Solving Approach

Abstract

In this paper, the problem of norm based reduced order approximations is investigated. The necessary and sufficient conditions for the existence of solution within a specified error is be found, in terms of a set of linear matrix inequalities (LMI) and  rank constraint for multi input-multi output systems. The projection algorithm and the complementarily algorithm used to solve the rank constraint. Numerical algorithms are proposed and a method of finding an initial starting point is suggested.