Optimization model for generic rank determination of structural matrices

Abstract

A simple and rigorous approach that determines the generic rank of a structural matrix is presented. This approach is based upon an integer linear programming (ILP) formulation which features the property of total unimodularity in the set of constraints. The integer linear programming formulation of the proposed approach with the addition of integer cuts can be used to identify all the structurally redundant equations and/or excess columns of a system. This approach can also be used as a systematic tool to search for all the possible (not necessarily feasible) sets of controlled and manipulated variables of large-scale control systems. The features of the proposed algorithm are illustrated through a representative set of example problems.