Accounting for singularities in design-results from a decoupling perspective

In this paper new results on decoupling in the presence of singularities, global decoupling and the effect of singularities on feedback linearization is presented. It is also argued that the decoupling problem bears an intimate relationship to many problems. This is demonstrated via relating a certain partial observability condition which appears in many situations to decoupling. In the process of establishing such connections many facts about decoupling (even in the regular setting) that have not been mentioned before in the literature is introduced. Finally the paper uses decoupling as a vantage point to outline a strategy to study of various design problems in the presence of singularities like a non-invertible decoupling matrix, a change in relative degree and vanishing control vector field for nonlinear systems