Abstract

This report explores asymptotic stability of nonlinear singular systems, i.e., differential algebraic equations with a descriptor state-space representation, by means of a polytopic rewriting of the "generalised characteristic polynomial" (determinant of the corresponding nonlinear pencil). It is shown that, via linearisation arguments, the Edge Theorem can be adapted for analysis purposes by taking into account that singularity of systems translates into degree dropping of some vertex polynomials.