Admissibility of Uncertain Injections in Quadratic Algebraic Systems

We study the admissibility problem in multivariate algebraic systems, such as ac electrical networks, where power injection is quadratic state. The goal of systems to ensure that state stays some security set (e.g., magnitudes nodal voltages and branch currents are within safety bounds). A common practice implicitly control by controlling injection; a difficulty number states correspond given can be zero or many. Further, subject uncertainty. whether it possible set, only available information uncertainty constrains injection. extend recently proposed V-control theory, design solution framework test if admissible, develop concrete method for networks.