  Projection-based control (PBC) systems have significant engineering impact
and receive considerable scientific attention. To properly describe closed-loop
PBC systems, extensions of classical projected dynamical systems are needed,
because partial projection operators and irregular constraint sets (sectors)
are crucial in PBC. These two features obstruct the application of existing
results on existence and completeness of solutions. To establish a rigorous
foundation for the analysis and design of PBC, we provide essential existence
and completeness properties for this new class of discontinuous systems.
