An algorithm to check the nonnegativity of singular systems

In the literature, an important class of generalized inverse matrices corresponds to the group inverse, that is, matrices of index 1. Recently, the nonnegativity of a singular system has been applied to different fields. In this paper, an algorithm to check the nonnegativity of a singular linear control system of index 1 is presented. To this purpose, the nonnegativity of this kind of systems is characterized using a block partition of the original matrices. In this way, we can work with matrices having smaller sizes and keeping the original information. Finally, numerical examples illustrating the obtained results are shown.