An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

Abstract

This paper deals with singular systems of index k ≥ 1. Our main goal is to find a state-feedback such that the closed-loop system satis- fies the regularity condition and it is nonnegative and stable. In order to do that, the core-nilpotent decomposition of a square matrix is applied to the singular matrix of the system. Moreover, if the Drazin projector of this matrix is nonnegative then the previous decomposition allows us to write the core-part of the matrix in a specific block form. In addition, an algorithm to study this kind of systems via a state-feedback is designed.